Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#12521 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C19 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C19 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ C82×C19 ◁ G | |
262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,27)(22,28,31,35)(23,32,29,26)(25,33,34,30)(37,41)(38,42)(39,45)(43,51)(44,49)(46,50)(47,48);(20,22,29,33,24,31,23,30)(21,25,32,35,27,34,26,28);(36,37,42,48,39,43,46,49,40,44,50,51,45,47,38,41)1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5509);