Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#13106 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C2×D4 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C8×D4 |
| prime radical | C23×C17 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C22×C16×C17 ◁ G | |
272 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)(20,23)(21,22)(24,25)(26,27,32,37,31,38,48,55,30,35,47,39,46,36,53,54)(28,29,42,44,41,45,52,57,40,33,49,50,56,43,34,51);(19,22)(23,25)(26,28,32,42,31,41,48,52,30,40,47,49,46,56,53,34)(27,33,37,50,38,43,55,51,35,29,39,44,36,45,54,57);(18,20,21,24)(19,23,22,25)(26,29,30,33)(27,34,35,52)(28,39,40,37)(31,45,46,43)(32,44,47,50)(36,49,38,42)(41,54,56,55)(48,57,53,51)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6094);