Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#7511 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C17 | C42 |
| commutator | C4 | C4×C16×C17 |
| Frattini, cosocle | C2×C32 | C22×C17 |
| socle | C2×C17 | #1397 |
| prime radical | C22×C17 | M64 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C16×C17 ◁ G | |
74 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)(18,19,20,26,21,28,32,47,22,29,33,48,35,51,56,72,23,30,34,45,36,52,57,68,38,53,58,69,59,74,76,80,24,27,31,46,37,49,54,70,39,50,55,71,60,73,75,81,40,25,41,42,61,43,63,65,62,44,64,66,77,67,78,79);(19,25,27,30)(20,31)(26,45,46,42)(28,43,49,52)(29,44,50,53)(32,54)(33,55)(34,41)(47,68,70,65)(48,69,71,66)(51,67,73,74)(56,75)(57,63)(58,64)(72,80,81,79)(76,78)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 499);