Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#7181 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #102 |
| commutator | C8 | C4×C8×C17 |
| Frattini, cosocle | C2×C4×C8 | C22×C17 |
| socle | C2×C17 | #1279 |
| prime radical | C23×C17 | #104 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
240 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,27,24,29,40,45,25,30,39,46,23,28,21,37)(20,31,33,42,35,48,32,26,36,41,49,43,34,47,38,44);(18,20,23,34,25,36,24,35)(19,26)(21,38,39,49,40,32,22,33)(27,41)(28,42)(29,43)(30,44)(31,46)(37,48)(45,47)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 169);