Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#2141 ⋊ C2 |
| Sylow | C79 ⋊ #13405 |
386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 87 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)(80,83,86,102)(81,88,91,118)(82,93)(84,104,106,100)(85,109,110,139)(87,111)(89,119,103,117)(90,122,123,138)(92,124)(94,129)(95,131)(96,127)(97,99)(98,134,135,107)(101,120,115,105)(108,140)(112,126)(113,141)(114,116)(121,136)(125,143)(128,132)(130,137)(133,142);(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)(83,99)(84,96)(85,108)(86,97)(88,116)(89,113)(90,121)(91,114)(92,103)(93,102)(94,106)(95,110)(98,133)(100,127)(101,128)(104,129)(105,130)(107,125)(109,131)(111,118)(112,123)(115,137)(117,141)(119,124)(120,132)(122,126)(134,142)(135,143)(136,138)(139,140);(80,81,86,91)(82,92,97,113)(83,98,102,135)(84,103,106,89)(85,107,110,134)(87,96,114,94)(88,115,118,101)(90,120,123,105)(93,126,99,136)(95,112,108,121)(100,138,104,122)(109,119,139,117)(111,140,116,131)(124,137,141,128)(125,130,142,132)(127,143,129,133)Polycyclic presentation:
2^8,79|a^2=h,c^2=dg,d^2=h,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,c^b=cf,d^b=dh,e^b=eh,i^b=i^78,d^c=dh,e^c=eg,f^c=fh,g^c=gh1282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 88896);