Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#2155 ⋊ C2 |
| Sylow | C79 ⋊ #13406 |
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,83,86,104)(81,88,92,117)(82,94)(84,103,106,101)(85,109,110,137)(87,111)(89,118,91,116)(90,120,122,134)(93,123)(95,100)(96,130)(97,126)(98,128)(99,121,132,107)(102,136,138,105)(108,135)(112,125)(113,115)(114,139)(119,142)(124,143)(127,131)(129,141)(133,140);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,82)(81,87)(83,100)(84,97)(85,108)(86,98)(88,115)(89,113)(90,119)(91,93)(92,114)(94,103)(95,106)(96,110)(99,125)(101,128)(102,135)(104,126)(105,129)(107,124)(109,127)(111,116)(112,122)(117,123)(118,139)(120,143)(121,140)(130,138)(131,136)(132,142)(133,134)(137,141);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,93)(83,99)(84,91)(85,107)(86,92)(87,95)(88,102)(89,106)(90,105)(94,125)(96,112)(97,114)(98,113)(100,133)(101,134)(103,120)(104,132)(108,119)(109,118)(110,121)(111,130)(115,141)(116,137)(117,138)(122,136)(123,127)(124,131)(126,143)(128,142)(129,140)(135,139)Polycyclic presentation:
2^8,79|c^2=dg,d^2=h,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,i^a=i^78,c^b=cf,d^b=dh,e^b=eh,f^b=fh,i^b=i^78,d^c=dh,e^c=eg,g^c=gh1288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 88907);