Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12606 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×C42 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | C2×#97 |
| prime radical | C24×C19 | M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ G | |
466 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)(26,36,38,45)(27,33)(28,42)(29,35)(30,32)(31,37,46,40)(34,43)(39,53,52,50)(41,49)(44,48)(47,54,55,51);(21,23)(24,26,28,39,29,40,44,54,30,38,43,52,27,37,41,51)(25,31,34,47,35,45,49,53,32,46,42,55,33,36,48,50);(25,32)(26,37,38,40)(28,43)(31,45,46,36)(33,35)(39,54,52,51)(41,44)(47,50,55,53)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5594);