Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33942 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#493 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×Q8×C17 ◁ C8×Q8×C17 ◁ G | |
486 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(23,24)(26,27,32,36)(28,33,31,47)(29,39,42,56)(30,43,46,55)(34,49,51,41)(35,38,53,45)(37,54,40,52)(44,48,57,50);(18,19,21,22)(20,24,25,23)(26,28,32,31)(27,33,36,47)(29,40,42,37)(30,38,46,45)(34,50,51,48)(35,43,53,55)(39,52,56,54)(41,57,49,44);(26,29,32,42)(27,34,36,51)(28,37,31,40)(30,44,46,57)(33,48,47,50)(35,52,53,54)(38,49,45,41)(39,55,56,43);(18,20,21,25)(19,23,22,24)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26930);