Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34326 |
| 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 | |
2128 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)(22,23,26,25)(24,28,29,27)(30,31)(32,39)(33,36)(34,42)(35,38)(37,43)(40,44)(41,45);(30,32,35,33)(31,36,38,39)(34,40,43,41)(37,44,42,45);(22,24,26,29)(23,27,25,28)(30,33,35,32)(31,36,38,39)(34,41,43,40)(37,44,42,45);(22,23,26,25)(24,27,29,28)(30,31)(32,39)(33,36)(34,37)(35,38)(40,45)(41,44)(42,43);(18,20,21,19)(22,25,26,23)(24,28,29,27)(30,34)(31,37)(32,40)(33,41)(35,43)(36,44)(38,42)(39,45)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27314);