Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#11963 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| prime radical | C17×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
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)(18,19,20,23,21,22,24,25)(26,27,31,36,29,38,45,35,32,37,48,53,46,34,30,47)(28,39,42,51,44,52,57,55,43,54,56,33,40,50,41,49);(19,22)(20,24)(26,28)(27,33)(29,40)(30,42)(31,41)(32,43)(34,49)(35,52)(36,54)(37,51)(38,55)(39,53)(44,46)(45,56)(47,50)(48,57);(19,22)(23,25)(26,29,32,46)(27,34,37,38)(28,40,43,44)(30,31,45,48)(33,49,51,55)(35,36,47,53)(39,52,54,50)(41,56,57,42)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4951);