Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#21043 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×M16×C17 ◁ G | |
790 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27,31,36,32,35,30,44)(28,33,40,47,38,48,39,54)(29,41,42,34,43,50,45,49)(37,51,53,46,52,56,55,57);(19,22)(23,25)(26,28,31,40,32,38,30,39)(27,33,36,47,35,48,44,54)(29,37,42,53,43,52,45,55)(34,46,50,56,49,57,41,51);(18,20,21,24)(19,23,22,25)(26,29)(27,34)(28,37)(30,45)(31,42)(32,43)(33,46)(35,49)(36,50)(38,52)(39,55)(40,53)(41,44)(47,56)(48,57)(51,54);(27,35)(28,38)(34,49)(36,44)(37,52)(39,40)(41,50)(53,55)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14031);