Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #13694 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#13732 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C19 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C19 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ C4×C8×C19 ◁ C4×C16×C19 ◁ G | |
146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 91 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25)(22,26,27,24)(28,29,31,35)(30,40,42,63)(32,49,46,76)(33,52,47,77)(34,53,48,39)(36,57,54,43)(37,60,55,41)(38,62,56,50)(44,74,70,91)(45,75,71,66)(51,80,68,79)(58,86,82,90)(59,73,81,85)(61,69,78,87)(64,84,88,67)(65,83,89,72);(20,22,23,27)(21,24,25,26)(29,35)(36,54)(37,55)(38,56)(39,53)(40,63)(49,76)(52,77)(58,82)(59,81)(61,78)(64,88)(65,89)(66,75)(74,91)(79,80);(28,30,41,67,33,44,68,85,48,71,87,86,62,83,46,57,31,42,60,84,47,70,51,73,34,45,69,90,50,72,32,43)(29,36,49,65,38,58,78,75,53,81,80,91,77,88,55,63,35,54,76,89,56,82,61,66,39,59,79,74,52,64,37,40)1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6720);