Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10764 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | C4×C22⋊C4 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C8×C19 ◁ G | |
1194 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 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)(26,34,36,30)(27,38,39,31)(28,33)(29,32)(35,42)(37,47,50,43)(40,51,52,44)(41,45)(46,49)(48,53)(54,55);(21,23)(24,26,28,37,29,36,41,50)(25,30,33,43,32,34,45,47)(27,35,40,48,39,49,52,55)(31,42,44,53,38,46,51,54);(24,27)(25,31)(26,35)(28,40)(29,39)(30,42)(32,38)(33,44)(34,46)(36,49)(37,48)(41,52)(43,53)(45,51)(47,54)(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, 3752);