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) = C22 |
| direct product | C17×#11987 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| prime radical | C23×C17 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
300 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)(19,23)(20,21)(24,25)(26,27,30,36,44,52,45,54,32,34,29,35,31,37,47,56)(28,38,40,51,48,55,43,33,42,50,39,57,41,53,46,49);(18,19)(20,23)(21,25)(22,24)(26,28,32,42)(27,33,34,49)(29,43,30,46)(31,48,44,41)(35,53,36,55)(37,57,52,51)(38,56,50,54)(39,47,40,45);(18,20,22,21)(19,23,24,25)(27,34)(33,49)(35,36)(37,52)(38,50)(51,57)(53,55)(54,56)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4975);