Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C24 |
| direct product | C2×C19×#1386 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #102 |
| commutator | C8 | C2×C42×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C24×C19 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
630 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(3,4,5,6)(7,8,11,15)(9,10,17,19)(12,14,20,22)(13,21,18,16);(7,9,12,16,13,14,19,15,11,17,20,21,18,22,10,8)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5554);