Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C2×C17×#2076 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C25×C17 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ C24×C4×C17 ◁ G | |
1270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(7,8)(9,12)(10,11)(13,14)(15,16,18,21,17,19,22,20);(3,4)(5,6)(8,11)(12,14)(16,19)(20,21);(4,6)(7,9,10,13)(8,12,11,14)(16,20)(18,22)(19,21)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16625);