Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34602 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| socle | C23×C17 | C25 |
| prime radical | C2×C17×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
2294 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)(20,21)(22,23)(24,27)(25,26)(28,29)(30,31)(32,35)(33,36)(34,37)(38,42)(39,43)(40,44)(41,45);(23,26)(27,29)(30,32,34,39)(31,35,37,43)(33,40,41,38)(36,44,45,42);(19,21)(30,33,34,41)(31,36,37,45)(32,38,39,40)(35,42,43,44);(31,37)(35,43)(36,45)(42,44);(22,24,25,28)(23,27,26,29)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27590);