Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C42 |
| direct product | C17×#14274 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C17 | C24 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
1742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,24,25)(31,35)(36,38)(37,43)(44,45);(26,27,28,29)(30,31,34,35)(32,38,40,36)(33,37,42,43)(39,45,41,44);(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,32,34,40)(31,36,35,38)(33,41,42,39)(37,45,43,44);(30,33,34,42)(31,37,35,43)(32,39,40,41)(36,44,38,45)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 7262);