Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#12014 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C2×D4 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C22×C17 | C2×C4⋊C8 |
| prime radical | C23×C17 | C4⋊C8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
220 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)(20,27)(21,25)(22,31)(23,26)(24,29)(28,32)(30,33)(34,35,37,41,38,42,47,53,39,43,48,54,49,55,59,63)(36,40,45,51,46,52,58,62,44,50,56,60,57,61,64,65);(18,20,22,29,23,30,21,28)(19,24,25,27,26,32,31,33)(34,36)(35,40)(37,45)(38,46)(39,44)(41,51)(42,52)(43,50)(47,58)(48,56)(49,57)(53,62)(54,60)(55,61)(59,64)(63,65);(18,21,23,22)(19,25,26,31)(20,28,30,29)(24,27,32,33)(36,44)(40,50)(45,56)(46,57)(51,60)(52,61)(58,64)(62,65)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5002);