Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #13392 |
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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:
(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)(80,83,84,100,86,102,106,103)(81,88,89,115,91,117,104,116)(82,93,94,124,97,99,96,129)(85,109,105,135,110,136,138,101)(87,111,92,121,113,141,114,143)(90,119,107,132,120,131,137,98)(95,127,126,125,108,139,128,134)(112,133,122,140,118,123,142,130);(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)(80,82)(81,87)(83,99)(84,96)(85,108)(86,97)(88,111)(89,114)(90,118)(91,113)(92,104)(93,102)(94,106)(95,110)(98,130)(100,124)(101,125)(103,129)(105,126)(107,122)(109,127)(112,120)(115,143)(116,121)(117,141)(119,123)(128,138)(131,133)(132,140)(134,135)(136,139)(137,142);(80,81)(82,92)(83,98)(84,104)(85,107)(86,91)(87,94)(88,101)(89,106)(90,105)(93,123)(95,112)(96,113)(97,114)(99,133)(100,131)(102,132)(103,119)(108,118)(109,116)(110,137)(111,139)(115,136)(117,135)(120,138)(121,125)(122,128)(124,140)(126,142)(127,141)(129,130)(134,143)Polycyclic presentation:
2^8,79|c^2=d,d^2=h,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,f^a=fh,g^a=gh,c^b=cf,d^b=dh,e^b=eh,e^c=egh,f^c=fh,g^c=gh,i^c=i^781288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 88804);