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) = C25 |
| direct product | C19×#33849 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
676 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,31,27)(26,36,38,51)(28,42,45,34)(29,41,48,33)(30,43,47,35)(32,44,37,39)(40,54,49,52)(46,53,55,50);(24,26)(25,32)(27,37)(28,44)(29,46)(30,49)(31,38)(33,51)(34,52)(35,53)(36,41)(39,45)(40,47)(42,54)(43,50)(48,55);(21,23)(24,27,31,25)(26,37,38,32)(28,41,45,33)(29,42,48,34)(30,43,47,35)(36,39,51,44)(40,53,49,50)(46,54,55,52);(24,28)(25,33)(26,38)(27,41)(29,47)(30,48)(31,45)(32,37)(34,43)(35,42)(36,54)(39,55)(44,46)(51,52)1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26837);