Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17547 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17616 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×Q8×C19 ◁ G | |
918 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(22,29)(23,27)(24,32)(25,28)(26,30)(31,34)(33,35)(37,41,43,46)(42,48,49,51);(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32)(36,37)(38,42)(39,46)(40,43)(41,47)(44,49)(45,51)(48,50);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(36,38)(37,42)(39,45)(40,44)(41,48)(43,49)(46,51)(47,50);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(38,44)(42,49)(45,50)(48,51)1159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10604);