Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C2×C42 |
| direct product | C17×#12622 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#99 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C22×D4 | C23×C17 |
| prime radical | C2×C17×#120 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C4×D4×C17 ◁ G | |
636 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 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)(22,23,26,28)(24,30,32,37)(25,29,34,36)(27,33,35,31);(22,24)(23,27)(25,33,34,31)(26,32)(28,35)(29,37,36,30);(18,20,21,19)(23,28)(27,35)(29,36)(30,37)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5610);