Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C2×C19×#1360 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| prime radical | C22×D8×C19 | C4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
434 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(3,4,5,8,6,7,9,10)(12,17,18,25)(13,21)(14,15)(19,22,20,26)(23,24);(4,7)(5,9)(11,12)(13,22)(14,20)(15,19)(16,18)(17,23)(21,25)(24,26)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4911);