Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33863 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3280 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25)(22,26,27,24)(28,29)(30,34)(31,35)(32,45)(33,38)(36,42)(37,43)(39,46)(40,55)(41,49)(44,51)(47,52)(48,53)(50,56)(54,58)(57,59);(20,22)(21,24)(23,27)(25,26)(28,30,33,41)(29,34,38,49)(31,39,44,54)(32,40,43,53)(35,46,51,58)(36,47,50,57)(37,48,45,55)(42,52,56,59);(29,35)(31,42)(32,43)(34,46)(36,37)(38,51)(39,52)(40,53)(44,56)(45,50)(47,48)(49,58)(54,59)(55,57);(22,27)(24,26)1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26851);