Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#13641 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C19 | C23 |
| commutator | C22 | C22×C16×C19 |
| Frattini, cosocle | C2×C16 | C23×C19 |
| socle | C22×C19 | C22×C16 |
| prime radical | C23×C19 | C2×C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C19 ◁ G | |
180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29,31,36,32,37,44,54,33,38,45,55,47,57,66,76,34,39,46,56,48,58,67,77,49,59,68,78,69,79,84,89)(30,35,41,51,42,52,63,73,43,53,64,74,65,75,83,88,40,50,60,70,61,71,80,85,62,72,81,86,82,87,90,91);(21,24)(25,27)(28,30)(29,35)(31,41)(32,42)(33,43)(34,40)(36,51)(37,52)(38,53)(39,50)(44,63)(45,64)(46,60)(47,65)(48,61)(49,62)(54,73)(55,74)(56,70)(57,75)(58,71)(59,72)(66,83)(67,80)(68,81)(69,82)(76,88)(77,85)(78,86)(79,87)(84,90)(89,91);(20,22,23,26)(21,25,24,27)(30,40)(35,50)(41,60)(42,61)(43,62)(51,70)(52,71)(53,72)(63,80)(64,81)(65,82)(73,85)(74,86)(75,87)(83,90)(88,91)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6629);