Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C19 · Schur multiplier (H2) = C42 |
| direct product | C19×#12541 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C42 |
| commutator | C4 | C43×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | C2×#97 |
| prime radical | C23×C19 | C2×M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ G | |
402 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)(24,25,27,31,28,33,39,47,29,32,40,46,41,48,54,55)(26,34,36,50,37,43,52,45,35,49,38,53,51,30,42,44);(24,26)(25,30,32,43)(27,38)(28,37)(29,35)(31,45,46,44)(33,34,48,49)(36,40)(39,42)(41,51)(47,53,55,50)(52,54);(20,21,22,23)(26,35)(30,43)(34,49)(36,38)(37,51)(42,52)(44,45)(50,53)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5529);