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) = C2×C4 |
| direct product | C17×#13122 |
| 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 | C2×#41×C17 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C22×C16×C17 ◁ G | |
326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(22,23,28,33,29,32,47,50,26,31,35,36,27,44,46,52)(24,34,39,51,40,45,49,53,37,25,41,43,38,42,30,48);(18,19,21,20)(22,24,35,41,29,40,46,30,26,37,28,39,27,38,47,49)(23,25,36,51,32,42,52,53,31,34,33,43,44,45,50,48);(18,20,21,19)(22,25,26,34)(23,30,31,49)(24,36,37,33)(27,45,29,42)(28,43,35,51)(32,39,44,41)(38,50,40,52)(46,53,47,48)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6110);