Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#23668 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C17×#117 ◁ G | |
874 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)(24,29)(25,27)(26,28)(30,31,35,37,34,39,33,38)(32,36,42,43,40,44,41,45);(18,19)(20,21)(22,24,26,25)(23,27,28,29)(30,32)(31,36)(33,41)(34,40)(35,42)(37,43)(38,45)(39,44);(19,21)(22,25,26,24)(23,27,28,29)(31,37)(33,35)(36,43)(38,39)(41,42)(44,45);(32,40)(36,44)(41,42)(43,45)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16656);