Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24274 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#25481 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×D4×C17 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C4×Q8×C17 ◁ G | |
770 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2176 |
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)(22,23,26,29)(24,28,25,27)(30,31,33,37,34,38,42,36)(32,35,41,44,40,43,39,45);(18,19)(20,21)(22,24,26,25)(23,27,29,28)(30,32,33,41,34,40,42,39)(31,35,37,44,38,43,36,45);(19,21)(31,36)(32,39)(33,42)(35,43)(37,38)(40,41);(22,25,26,24)(23,28,29,27)(32,40)(35,43)(39,41)(44,45)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18469);