Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33516 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C22×C19 | C22×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
1150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 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)(26,35)(27,32)(28,40)(29,44)(30,34)(31,37)(33,42)(36,51)(38,52)(39,50)(41,46)(43,54)(45,49)(47,55)(48,53);(24,26)(25,31)(27,36)(28,41)(29,45)(30,38)(32,46)(33,49)(34,48)(35,40)(37,42)(39,53)(43,55)(44,47)(50,51)(52,54);(21,23);(24,27,30,29)(25,32,34,44)(26,36,38,45)(28,39,43,42)(31,46,48,47)(33,40,50,54)(35,51,52,49)(37,41,53,55)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26504);