Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#10900 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #386 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
686 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)(20,21,23,22)(24,25)(26,35)(27,40)(28,44)(29,33)(30,34)(31,37)(32,42)(36,51)(38,47)(39,46)(41,49)(43,48)(45,53)(50,52)(54,55);(24,26,29,37,30,39,28,38)(25,31,33,46,34,47,44,35)(27,36,42,52,43,53,41,54)(32,45,48,55,49,51,40,50);(20,22,23,21)(24,27)(25,32)(26,36)(28,41)(29,42)(30,43)(31,45)(33,48)(34,49)(35,50)(37,52)(38,54)(39,53)(40,44)(46,55)(47,51)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3888);