Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#17314 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | C24 |
| commutator | C2 | C22×C4×C8×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C22×C42 |
| prime radical | C24×C17 | C42 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ G | |
914 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(26,27,29,33,30,32,36,39)(28,31,35,38,34,37,40,41);(18,19,20,22,21,23,24,25)(26,28)(27,31)(29,35)(30,34)(32,37)(33,38)(36,40)(39,41);(28,34)(31,37)(35,40)(38,41);(27,32)(31,37)(33,39)(38,41)2312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10302);