Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#11498 |
| 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 | C23×C17 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
292 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26,28,23)(21,24)(22,25)(27,32,33,30)(29,31)(34,35,39,45,41,44,54,62,40,46,53,63,38,55,37,43)(36,47,50,61,49,42,48,58,51,60,64,57,56,59,52,65);(18,20,22,28)(19,23,25,26)(21,27,29,33)(24,30,31,32)(34,36,40,51)(35,42,46,59)(37,52,54,48)(38,56,41,49)(39,50,53,64)(43,61,62,57)(44,60,55,47)(45,58,63,65);(18,21,22,29)(19,24,25,31)(20,27,28,33)(23,30,26,32)(34,37,38,53,40,54,41,39)(35,43,55,63,46,62,44,45)(36,48,56,50,51,52,49,64)(42,57,47,58,59,61,60,65)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4486);