Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#362×C79 ⋊ C2 |
| Sylow | C79 ⋊ #13339 |
534 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 147 points:
(1,2)(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)(81,83)(84,87)(85,93)(86,99)(88,113)(89,109)(90,108)(91,110)(92,118)(94,128)(95,125)(96,124)(97,126)(98,131)(100,138)(101,136)(102,105)(103,137)(104,111)(106,114)(107,115)(112,135)(116,144)(117,143)(119,142)(120,122)(121,146)(123,129)(127,140)(130,141)(132,145)(133,147)(134,139);(80,81)(82,83)(84,86,91,103)(85,92,97,121)(87,105,110,136)(88,112,116,139)(89,102,90,101)(93,122,126,142)(94,127,130,132)(95,120,96,119)(98,129,133,111)(99,109,137,108)(100,114,117,115)(104,140,123,145)(106,134,107,135)(113,143,144,138)(118,125,146,124)(128,147,141,131);(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)(84,85,91,97)(86,98,103,133)(87,104,110,123)(88,111,116,129)(89,96,90,95)(92,117,121,100)(93,106,126,107)(94,114,130,115)(99,118,137,146)(101,127,102,132)(105,142,136,122)(108,128,109,141)(112,119,139,120)(113,124,144,125)(131,134,147,135)(138,140,143,145)Polycyclic presentation:
2^8,79|a^2=h,b^2=h,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fh,g^a=gh,i^a=i^78,c^b=cf,d^b=dg,e^b=eg,f^b=fh,g^b=gh,d^c=dgh,e^c=eg,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, 88487);