Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11663 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12817 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25)(26,34,35,50)(27,30)(28,40)(29,43)(31,36,45,53)(32,42)(33,39)(37,48,44,52)(38,51)(41,49,55,47)(46,54);(20,21,22,23)(25,30)(31,45)(32,46)(33,43)(34,50)(40,51)(47,49)(48,52);(24,26)(25,31)(27,35)(28,41)(29,44)(30,45)(32,48)(33,49)(34,51)(36,54)(37,39)(38,55)(40,50)(42,53)(43,47)(46,52)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5805);