Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#20944 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1702 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
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)(21,23)(24,25,29,33,30,35,28,34)(26,36,38,31,40,46,39,47)(27,41,43,32,44,48,42,49)(37,45,51,54,53,55,52,50);(20,21,22,23)(24,26)(25,31)(27,37)(28,38)(29,39)(30,40)(32,45)(33,36)(34,46)(35,47)(41,54)(42,51)(43,52)(44,53)(48,50)(49,55);(24,27)(25,32)(26,37)(28,42)(29,43)(30,44)(31,45)(33,48)(34,41)(35,49)(36,50)(38,51)(39,52)(40,53)(46,54)(47,55);(24,28,30,29)(25,33,35,34)(26,38,40,39)(27,42,44,43)(31,36,47,46)(32,48,49,41)(37,51,53,52)(45,50,55,54)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13932);