Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#11470 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×C22⋊C8 |
| prime radical | C17×#525 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C8×C17 ◁ G | |
392 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(20,24,25,22)(21,23)(26,27,31,37,32,38,45,52,33,39,29,35,30,36,46,53)(28,40,43,56,42,51,57,49,44,54,41,55,47,34,48,50);(18,20)(19,22)(21,25)(23,24)(26,28)(27,34)(29,43)(30,47)(31,41)(32,42)(33,44)(35,50)(36,54)(37,49)(38,40)(39,51)(45,48)(46,57)(52,55)(53,56);(26,29,32,46,33,31,30,45)(27,35,38,53,39,37,36,52)(28,41,42,48,44,43,47,57)(34,49,40,55,51,50,54,56)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4458);