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) = C22×C42 |
| direct product | C19×#10699 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C42 |
| commutator | C4 | C43×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #376 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ G | |
842 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)(26,36,39,46)(27,32)(28,33)(29,35)(30,34)(31,38,45,40)(37,50,52,55)(41,47)(42,49)(43,48)(44,51,54,53);(21,23)(24,26)(25,31,34,45)(27,37)(28,38)(29,40)(30,39)(32,44,48,54)(33,36,35,46)(41,51)(42,53)(43,52)(47,50,49,55);(24,27,29,42,30,43,28,41)(25,32,35,49,34,48,33,47)(26,37,40,53,39,52,38,51)(31,44,46,55,45,54,36,50)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3687);