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×#21659 |
| 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×C17×#97 ◁ G | |
722 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)(26,27,32,37,33,38,31,49)(28,39,43,51,44,55,42,34)(29,45,30,36,47,53,46,35)(40,52,48,57,56,50,41,54);(19,22)(23,25)(26,28,31,42,33,44,32,43)(27,34,37,39,38,51,49,55)(29,40,46,41,47,56,30,48)(35,50,45,54,36,52,53,57);(18,20,21,24)(19,23,22,25)(26,29,31,46,33,47,32,30)(27,35,37,45,38,36,49,53)(28,40,42,41,44,56,43,48)(34,50,39,54,51,52,55,57);(26,30,32,47,33,46,31,29)(27,36,37,53,38,35,49,45)(28,41,43,40,44,48,42,56)(34,50,39,54,51,52,55,57)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14647);