Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#21548 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C2×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C17×#3054 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C23×C8×C17 ◁ G | |
914 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)(18,19)(20,21)(22,23,27,31,28,32,26,41)(24,33,37,42,34,46,36,29)(25,30,39,44,40,45,38,51)(35,47,50,52,48,53,49,43);(22,24,26,36,28,34,27,37)(23,29,31,33,32,42,41,46)(25,35,38,49,40,48,39,50)(30,43,44,47,45,52,51,53);(19,21)(24,34)(29,42)(33,46)(35,48)(36,37)(43,52)(47,53)(49,50);(22,25,27,39,28,40,26,38)(23,30,31,44,32,45,41,51)(24,35,37,50,34,48,36,49)(29,43,33,47,42,52,46,53)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14536);