Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C25 |
| direct product | C2×C17×#1270 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C22⋊C4 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×D4×C17 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ C22×C42×C17 ◁ G | |
994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2176 |
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)(13,15)(14,17)(16,18)(19,20,21,23,22,24,25,26);(3,5)(4,7)(6,10)(8,9)(12,15)(13,18)(16,17)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 546);