Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#11406 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C42 |
| commutator | C4 | C2×C4×C8×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| socle | C22×C19 | C2×#97 |
| prime radical | C23×C19 | #97 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ G | |
282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(28,29,31,36,32,37,43,52,33,35,44,49,45,50,58,59)(30,38,40,53,41,48,56,51,39,54,42,57,55,34,46,47);(20,21,22,24,23,25,26,27)(28,30)(29,34,35,48)(31,42)(32,41)(33,39)(36,51,49,47)(37,38,50,54)(40,44)(43,46)(45,55)(52,57,59,53)(56,58);(29,35)(30,39)(36,49)(37,50)(40,42)(41,55)(46,56)(52,59)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4394);