Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C211 |
| direct product | C23×C17×#99 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C22⋊C4 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C24×D4×C17 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ C26×C17 ◁ G | |
7902 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4);(5,6);(7,8)(9,13,14,11)(10,12);(7,9)(8,11)(10,14)(12,13)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53054);