Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10500 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#10506 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,28)(22,29,31,26)(23,25,32,27)(30,34,35,33)(36,37)(38,41)(39,42)(40,44)(43,48)(45,49)(46,51)(47,50);(21,25)(22,30)(23,32)(26,29)(27,28)(31,35)(36,38,40,46)(37,41,44,51)(39,47,48,45)(42,50,43,49);(20,22,23,30,24,31,32,35)(21,26,27,34,28,29,25,33)(37,42)(39,48)(41,49)(43,44)(45,47)(50,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3494);