Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#22889 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C19×#3002 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C19×C22⋊C8 ◁ G | |
1020 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)(24,25,29,33,30,34,28,42)(26,35,37,31,38,46,43,47)(27,32,41,51,40,49,44,50)(36,48,39,45,52,55,53,54);(24,26,29,37,30,38,28,43)(25,31,33,46,34,47,42,35)(27,39,41,52,40,53,44,36)(32,48,51,45,49,55,50,54);(21,23)(27,40)(32,49)(36,52)(39,53)(41,44)(45,54)(48,55)(50,51);(24,27)(25,32)(26,36)(28,44)(29,41)(30,40)(31,45)(33,51)(34,49)(35,48)(37,39)(38,52)(42,50)(43,53)(46,55)(47,54)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15877);