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×#17724 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3508 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×#41×C19 ◁ G | |
1004 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)(20,21,23,27,24,25,30,32)(22,26,29,33,28,31,34,35)(36,37)(38,42)(39,41)(40,44)(43,47)(45,49)(46,48)(50,51);(21,25)(23,30)(26,31)(29,34)(37,41)(39,47)(42,48)(43,44)(46,51)(49,50);(20,22)(21,26)(23,29)(24,28)(25,31)(27,33)(30,34)(32,35)(36,38,40,45)(37,42,44,49)(39,46,47,51)(41,48,43,50);(22,28)(26,31)(29,34)(33,35)(38,45)(42,49)(46,51)(48,50)1159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10712);