Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33388 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33392 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×#102 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#576 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
1154 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(20,21,24,29,25,31,39,30)(22,27,34,44,32,42,47,45)(23,35,37,28,38,26,36,41)(33,48,50,43,46,40,49,51);(21,26)(23,36)(24,39)(27,40)(28,29)(30,41)(31,35)(33,49)(34,47)(37,38)(42,48)(43,44)(45,51)(46,50);(20,22)(21,27)(23,33)(24,34)(25,32)(26,40)(28,43)(29,44)(30,45)(31,42)(35,48)(36,49)(37,50)(38,46)(39,47)(41,51);(22,32)(27,42)(33,46)(34,47)(40,48)(43,51)(44,45)(49,50)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26380);