Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1705 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C8 |
| direct product | C2×C17×#1709 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C2×C17×#493 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
982 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);(4,5)(6,7)(9,10)(11,12)(13,19)(14,22)(15,17)(16,20)(18,23)(21,25)(24,26);(3,4,7,9,8,10,6,5)(11,13,14,20,15,21,23,26)(12,16,18,19,17,24,22,25);(3,5,6,10,8,9,7,4)(12,17)(16,24)(18,22)(19,25)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12585);