Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C32 · Schur multiplier (H2) = C2 |
| direct product | C17×#7513 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C17 | C22⋊C4 |
| commutator | C22 | C2×C17×C32 |
| Frattini, cosocle | C2×C32 | C22×C17 |
| socle | C2×C17 | C22⋊C32 |
| prime radical | C23×C17 | C32 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C17 ◁ C2×C17×C32 ◁ G | |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,26,21,27,31,44,22,28,32,45,34,47,53,66,23,29,33,46,35,48,54,67,37,49,55,68,56,69,73,79,24,25,30,40,36,41,50,60,38,42,51,61,57,63,70,75,39,43,52,62,58,64,71,76,59,65,72,77,74,78,80,81);(19,25)(20,30)(27,41)(28,42)(29,43)(31,50)(32,51)(33,52)(47,63)(48,64)(49,65)(53,70)(54,71)(55,72)(69,78)(73,80)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 501);