Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11858 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#11894 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24,25,22)(21,23)(26,27,31,37,33,39,32,38)(28,40,43,55,45,56,44,51)(29,46,30,49,48,36,47,35)(34,50,52,42,54,41,53,57);(18,20)(19,22)(21,25)(23,24)(26,28)(27,34)(29,42)(30,50)(31,44)(32,43)(33,45)(35,40)(36,55)(37,53)(38,52)(39,54)(41,47)(46,51)(48,57)(49,56);(20,25)(22,24)(26,29,32,47,33,48,31,30)(27,35,37,46,39,49,38,36)(28,41,44,42,45,50,43,57)(34,51,52,40,54,55,53,56)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4882);