Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C2×C17×#1347 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#466 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 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)(5,9,10,7)(6,8)(11,12)(13,16)(14,23)(15,19)(17,20)(18,21)(22,25)(24,26);(3,5)(4,7)(6,10)(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, 4689);