Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#20917 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C8×C19 ◁ G | |
1698 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)(26,36,40,47)(27,41,44,49)(28,34)(29,35)(30,33)(31,38,46,39)(32,43,48,42)(37,51)(45,54)(50,52)(53,55);(20,21,22,23)(24,26,28,39,30,40,29,38)(25,31,34,47,33,46,35,36)(27,37,43,52,44,54,42,53)(32,45,41,55,48,51,49,50);(24,27)(25,32)(26,37)(28,43)(29,42)(30,44)(31,45)(33,48)(34,41)(35,49)(36,50)(38,53)(39,52)(40,54)(46,51)(47,55);(25,33)(31,46)(32,48)(34,35)(36,47)(41,49)(45,51)(50,55)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13905);