Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60209 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C24×C4 |
| prime radical | C17×#3455 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
1878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 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)(26,27,30,35,31,34,41,47)(28,32,38,44,37,43,50,54)(29,33,40,46,39,45,51,55)(36,42,48,53,49,52,56,57);(19,22)(23,25)(26,28)(27,32)(29,36)(30,38)(31,37)(33,42)(34,43)(35,44)(39,49)(40,48)(41,50)(45,52)(46,53)(47,54)(51,56)(55,57);(26,29,30,40,31,39,41,51)(27,33,35,46,34,45,47,55)(28,36,38,48,37,49,50,56)(32,42,44,53,43,52,54,57);(18,20,21,24)(19,23,22,25)(28,37)(29,39)(32,43)(33,45)(38,50)(40,51)(44,54)(46,55);(27,34)(32,43)(33,45)(35,47)(42,52)(44,54)(46,55)(53,57)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53197);