Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C2×C17×#2226 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C22×D8×C17 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
638 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(3,4,6,8)(5,9,10,7)(11,12,15,19)(13,16,22,25)(14,23,21,18)(17,26,24,20);(3,5,6,10)(4,7,8,9);(12,16)(13,20)(14,21)(17,18)(19,25)(22,26)(23,24)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26609);