Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #13694 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13731 |
| 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 | |
158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4864 |
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)(20,21,23,25)(22,26,27,24)(29,34)(30,35)(31,39)(32,42)(36,51)(37,54)(38,47)(40,56)(41,50)(43,55)(44,45)(46,52)(48,49)(53,59)(57,58);(20,22,23,27)(21,24,25,26);(28,29,35,45,31,36,48,54,42,52,56,59,55,57,41,47,33,38,50,58,43,53,40,46,32,37,49,51,39,44,30,34)1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6719);