Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17855 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C4 | C23×C8×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C22×D4×C17 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C17×#431 ◁ G | |
730 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)(18,19,21,24,22,20,23,25)(26,27)(28,34)(29,37)(30,32)(31,35)(33,39)(36,41)(38,40);(26,28,30,36)(27,31,32,40)(29,38,39,35)(33,41,37,34);(18,20,21,25,22,19,23,24)(26,27)(28,31)(29,33)(30,32)(34,35)(36,40)(37,39)(38,41);(27,32)(31,40)(33,37)(34,41)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10843);