Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#13288 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,22)(23,25)(26,27)(28,38,43,53)(29,44)(30,34)(31,48)(32,37)(33,41,51,46)(35,39)(36,45)(40,50,55,57)(42,49,56,54)(47,52);(19,22)(23,24)(26,28,39,55,45,56,30,46,32,43,29,40,31,42,47,41)(27,33,34,49,48,57,35,53,37,51,52,54,36,50,44,38);(18,20,21,25)(19,23,22,24)(26,29,45,47,32,39,31,30)(27,34,48,35,37,52,36,44)(28,40,56,41,43,55,42,46)(33,49,57,53,51,54,50,38)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6276);