Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25×C4 |
| direct product | C17×#21224 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C2×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C23×C17 | C22×D4 |
| prime radical | C22×C17×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ C22×C42×C17 ◁ G | |
1622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,24,25)(26,27)(28,38)(29,41)(30,35)(31,36)(32,37)(33,39)(34,40);(18,19,20,21)(23,25)(26,28,30,39,32,40,31,29)(27,33,36,38,37,41,35,34);(26,29,31,40,32,39,30,28)(27,34,35,41,37,38,36,33);(26,30,32,31)(27,35,37,36)(28,39,40,29)(33,34,41,38)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14212);