Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C2×C17×#2929 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C17 | C23 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C23×C17 | C23×C4 |
| prime radical | C2×C17×#525 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C17 ◁ G | |
3046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4)(5,6)(7,8,10,14,11,13,17,20)(9,12,15,19,16,18,21,22);(4,6);(7,9,10,15,11,16,17,21)(8,12,14,19,13,18,20,22);(8,13)(12,18)(14,20)(19,22)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53121);