Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#11939 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C22×C17 | C2×#102 |
| prime radical | C23×C17 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
306 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)(19,22)(20,24)(23,25)(26,27,31,36,29,34,44,35,32,37,47,52,45,53,30,46)(28,38,41,50,43,54,57,48,42,55,56,33,39,49,40,51);(18,19,21,23)(20,25,24,22)(26,28,32,42)(27,33,37,50)(29,39,45,43)(30,41,44,56)(31,40,47,57)(34,48,53,51)(35,54,46,49)(36,55,52,38);(26,29,32,45)(27,34,37,53)(28,39,42,43)(30,31,44,47)(33,48,50,51)(35,52,46,36)(38,49,55,54)(40,56,57,41)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4927);