Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#20514 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C4 | C22×C42×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C17×#97 ◁ G | |
998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,27,32,28,30,26,41)(24,33,35,29,36,45,42,43)(25,37,40,52,38,31,39,46)(34,48,50,51,49,47,53,44);(18,19,21,20)(22,24)(23,29)(25,34)(26,42)(27,35)(28,36)(30,43)(31,44)(32,45)(33,41)(37,51)(38,49)(39,53)(40,50)(46,48)(47,52);(18,20,21,19)(23,30)(25,38)(29,43)(32,41)(33,45)(34,49)(39,40)(50,53);(22,25,27,40,28,38,26,39)(23,31,32,46,30,37,41,52)(24,34,35,50,36,49,42,53)(29,44,45,48,43,51,33,47)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13502);