Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17391 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×Q8×C19 ◁ G | |
876 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,26,24,27,30,33)(22,25,29,32,28,31,34,35)(36,37)(38,46,49,42)(39,43)(40,44)(41,45)(47,60,63,54)(48,61,65,55)(50,56)(51,57)(52,58)(53,59)(62,67,64,66);(20,22)(21,25)(23,29)(24,28)(26,32)(27,31)(30,34)(33,35)(36,38,41,49)(37,42,45,46)(39,47,51,63)(40,48,53,65)(43,54,57,60)(44,55,59,61)(50,62,52,64)(56,66,58,67);(22,28)(25,31)(29,34)(32,35)(36,39,41,51)(37,43,45,57)(38,47,49,63)(40,52,53,50)(42,54,46,60)(44,58,59,56)(48,64,65,62)(55,67,61,66);(36,40,41,53)(37,44,45,59)(38,48,49,65)(39,50,51,52)(42,55,46,61)(43,56,57,58)(47,62,63,64)(54,66,60,67)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10379);