Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#14442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C24 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
1650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2176 |
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)(19,20)(26,27,28,29)(30,31)(32,34)(33,35)(36,37);(23,25)(31,32)(33,37);(18,19,21,20)(22,23,24,25)(30,32,34,31)(33,36,37,35);(18,20,21,19)(30,33)(31,35)(32,36)(34,37)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 7430);