Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13180 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #459 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23)(24,34)(25,31)(26,41)(27,44)(28,33)(29,35)(30,39)(32,43)(36,49)(37,51)(38,45)(40,50)(42,46)(47,52)(48,53);(18,20,21,19)(22,24)(23,29)(25,35)(26,42)(27,36)(28,38)(30,45)(31,49)(32,46)(33,48)(34,41)(37,43)(39,52)(40,53)(44,47)(50,51);(22,25,27,39,28,40,43,26)(23,30,32,31,33,41,44,50)(24,35,36,52,38,53,37,42)(29,45,46,49,48,34,47,51)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6168);