Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C22×C42 |
| direct product | C17×#14668 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C17 | C24 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
1102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
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)(23,26)(27,29)(30,31,34,32)(33,35,37,36)(38,39,42,43)(40,44,45,41);(18,19,20,21)(24,28)(27,29)(31,32)(33,37)(40,45)(41,44);(22,23)(24,27)(25,26)(28,29)(30,32,34,31)(33,35,37,36)(38,40)(39,41)(42,45)(43,44);(22,24)(23,27)(25,28)(26,29)(30,33,34,37)(31,35,32,36)(38,41)(39,40)(42,44)(43,45)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 7656);