Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #12596 |
310 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 115 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)(84,87,88,89,90,104,105,106)(85,92,93,111,95,94,96,102)(86,98,99,113,101,103,114,100)(91,107,97,112,108,110,109,115);(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)(80,81,82,83)(84,86)(85,91,95,108)(87,103)(88,99)(89,100)(90,101)(92,110,94,107)(93,97,96,109)(98,104)(102,112,111,115)(105,114)(106,113);(84,85,89,94,88,96,104,111,90,95,106,92,105,93,87,102)(86,97,100,112,99,91,98,107,101,109,113,115,114,108,103,110)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=d,d^2=h,e^2=g,g^2=h,b^a=bd,c^a=cg,d^a=dh,f^a=fh,c^b=ch,i^b=i^78,e^c=eh,i^c=i^781780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 84587);