Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1714 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C8 |
| direct product | C2×C17×#1721 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
1146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(4,7)(5,9)(8,10)(12,15)(13,16)(17,18);(3,4,5,7,6,8,9,10);(4,8)(7,10)(11,12,16,18,14,17,13,15)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12602);