Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17777 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| prime radical | C2×#41×C19 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×#41×C19 ◁ G | |
900 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,27,24,26,32,34)(22,28,29,35,30,25,31,33)(36,37)(38,47)(39,44)(40,45)(41,50)(42,46)(43,48)(49,51);(20,22,24,30)(21,25,26,28)(23,31,32,29)(27,35,34,33)(36,38,42,39)(37,43,46,51)(40,48,41,49)(44,50,47,45);(36,39,42,38)(37,44,46,47)(40,48,41,49)(43,50,51,45);(36,40,42,41)(37,45,46,50)(38,48,39,49)(43,44,51,47)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10765);