Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#7288 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #102 |
| commutator | C2×C8 | C42×C19 |
| Frattini, cosocle | C2×C4×C8 | C22×C19 |
| socle | C22×C19 | #340 |
| prime radical | C23×C19 | #107 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
202 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 2 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,26,24,27,31,34)(22,28,30,35,29,25,32,33)(37,42)(38,46)(39,48)(40,47)(43,44)(45,51)(49,50);(20,22)(21,25,27,28)(23,30)(24,29)(26,33,34,35)(31,32)(36,37,39,43,40,44,38,42,41,45,46,50,47,49,48,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 276);