Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#21663 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C17×#532 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
730 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(18,19)(20,23)(21,22)(24,25)(26,27,31,38,33,39,32,37)(28,40,43,34,45,53,44,54)(29,46,30,36,49,55,48,35)(41,51,42,57,47,52,50,56);(19,22)(23,25)(26,28,32,44,33,45,31,43)(27,34,38,53,39,54,37,40)(29,47,48,42,49,41,30,50)(35,52,46,56,36,51,55,57);(18,20,21,24)(19,23,22,25)(26,29,31,30,33,49,32,48)(27,35,37,55,39,36,38,46)(28,41,43,42,45,47,44,50)(34,51,40,56,54,52,53,57);(26,30,31,49,33,48,32,29)(27,36,38,55,39,35,37,46)(28,42,43,47,45,50,44,41)(34,52,53,56,54,51,40,57)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14651);