Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#21004 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,27,29,26,25,31,34)(24,30,33,37,32,28,35,36);(22,24,31,33,26,32,27,35)(23,28,29,37,25,30,34,36);(19,21)(22,25)(23,26)(24,30)(27,29)(28,32)(31,34)(33,36)(35,37);(24,32)(28,30)(33,35)(36,37)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13992);