Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#60170 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator | C4 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C2×C17×#575 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C17×#117 ◁ G | |
2742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23)(24,29)(25,30)(26,35)(27,31)(28,32)(33,36)(34,37);(22,24)(23,28)(25,32)(26,34)(27,33)(29,35)(30,36)(31,37);(18,20,21,19)(22,24)(23,29)(25,34)(26,32)(27,33)(28,35)(30,37)(31,36);(22,25,27,26)(23,30,31,35)(24,32,33,34)(28,36,37,29);(23,31)(28,37)(29,36)(30,35)1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53158);