Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#8649 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | #121 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
438 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)(18,19,20,21)(23,26)(24,27)(28,29)(30,31)(32,38)(33,35)(34,42)(36,40)(37,41)(39,45)(43,44);(22,23,27,29,25,28,24,26)(31,35)(36,44)(37,42)(38,45);(30,32,33,39)(31,36,35,44)(34,43,41,40)(37,45,42,38)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1637);