Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#22050 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G | |
996 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)(18,19,21,20)(22,23)(24,28)(25,27)(26,29)(30,31,34,37)(32,38,39,45)(33,41,43,36)(35,42,44,40);(18,20,21,19)(22,24)(23,26)(25,29)(27,28)(32,39)(35,44)(38,45)(40,42);(24,29)(26,28)(30,32,34,39)(31,35,37,44)(33,42,43,40)(36,45,41,38);(23,27)(26,28)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15038);