Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #14715 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×C22⋊#401 |
| unambiguous semidirect product | C22⋊(C17×#401) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C17 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
1650 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)(19,21)(22,23,25,27)(24,26,28,29)(30,31,34,35)(32,37,36,33)(38,39)(40,43)(41,45)(42,44);(24,28)(26,29)(31,35)(32,36)(38,40,42,45)(39,43,44,41);(22,24)(23,26)(25,28)(27,29)(30,32,34,36)(31,33,35,37)(38,40)(39,41)(42,45)(43,44);(18,19)(20,21)(22,23)(24,26)(25,27)(28,29)(30,33)(31,36)(32,35)(34,37)(38,41)(39,40)(42,43)(44,45)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 7815);