Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13452 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,26,28)(24,29,25,27)(30,31,33,38)(32,40,35,36)(34,37,42,45)(39,41,44,43);(18,19)(20,21)(22,24,26,25)(23,27,28,29)(30,32,33,35)(31,36,38,40)(34,41,42,43)(37,39,45,44);(19,21)(22,25,26,24)(23,27,28,29)(31,37)(32,35)(34,43)(36,44)(38,45)(39,40)(41,42)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6440);