Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#17605 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#525 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C19×#117 ◁ G | |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(22,30,33,26)(23,27)(24,28)(25,29)(31,35,32,34)(37,41,43,46)(42,48,49,51);(20,22)(21,26)(23,31)(24,32)(25,33)(27,34)(28,35)(29,30)(36,37)(38,42)(39,46)(40,43)(41,47)(44,49)(45,51)(48,50);(20,23,25,24)(21,27,29,28)(22,31,33,32)(26,34,30,35)(36,38)(37,42)(39,45)(40,44)(41,48)(43,49)(46,51)(47,50);(20,24,25,23)(21,28,29,27)(22,32,33,31)(26,35,30,34)(38,44)(42,49)(45,50)(48,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10593);