Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C210 |
| direct product | C22×C4×D8×C17 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C17 | D4 |
| commutator | C4 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C24×C17 | C2×D4 |
| prime radical | C23×D8×C17 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C17 ◁ C22×C42×C17 ◁ G | |
3694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(3,4);(5,6,7,8);(9,10,11,12,13,14,15,16);(10,16)(11,15)(12,14)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53136);