Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C2×C17×#1637 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C22×D4×C17 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
1174 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);(3,4,6,9)(5,7,10,8)(11,12,17,21)(13,22,14,25)(15,20,16,19)(18,24,26,23);(4,7)(5,10)(8,9)(11,13,17,14)(12,18,21,26)(15,24,16,23)(19,25,20,22);(11,14,17,13)(12,18,21,26)(15,23,16,24)(19,25,20,22)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11477);