Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C79×#2846 ⋊ C2 |
| Sylow | C79 ⋊ #36714 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D79 |
| commutator, socle, cosocle | C23×C79 | C25 |
| Fitting | C79×#2846 | C2 |
| hypercenter | #2846 | D79 |
| hypocenter | C79 | #36714 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #2846 | |
4170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 5 generators on 99 points:
(6,10)(9,11)(14,18)(17,20)(21,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23);(6,10)(7,12)(15,19)(17,20);(2,4)(15,19)(17,20);(5,7)(6,9)(8,12)(10,11)(13,15)(14,17)(16,19)(18,20)(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)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99);(1,2,3,4)(5,6)(7,11)(8,10)(9,12)(13,14)(15,17)(16,18)(19,20)Polycyclic presentation:
2^8,79|a^2=g,b^a=bf,c^a=cg,d^a=df,e^a=efh,c^b=ch,d^b=dfh,i^b=i^781768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 376490);