Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34487 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C22×D4×C17 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2244 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23,26,24)(25,28,29,27)(31,35)(32,38)(33,41)(43,45);(23,24)(27,28)(30,31,34,35)(32,39,38,36)(33,37,41,42)(40,45,44,43);(30,32,34,38)(31,36,35,39)(33,40,41,44)(37,43,42,45);(18,20,21,19)(22,24,26,23)(25,28,29,27)(30,31)(32,36)(33,37)(34,35)(38,39)(40,43)(41,42)(44,45);(22,25,26,29)(23,27,24,28)(30,33,34,41)(31,37,35,42)(32,40,38,44)(36,43,39,45)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27475);