Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#21372 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C22×C4⋊C4 |
| prime radical | C24×C17 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C17×#117 ◁ G | |
714 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)(26,27,31,35,32,36,30,44)(28,37,39,33,40,47,45,48)(29,34,43,50,41,49,42,54)(38,51,53,46,52,57,55,56);(26,28,31,39,32,40,30,45)(27,33,35,47,36,48,44,37)(29,38,43,53,41,52,42,55)(34,46,50,57,49,56,54,51);(19,22)(23,25)(26,29)(27,34)(28,38)(30,42)(31,43)(32,41)(33,46)(35,50)(36,49)(37,51)(39,53)(40,52)(44,54)(45,55)(47,57)(48,56);(18,20,21,24)(19,23,22,25)(29,41)(34,49)(38,52)(42,43)(46,56)(50,54)(51,57)(53,55)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14360);