Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#12002 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #106 |
| commutator | C8 | C22×C8×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C2×C17 | C2×#334 |
| prime radical | C23×C17 | #108 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
220 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,28,24,29,39,45,25,30,38,27,23,41,21,37)(20,31,34,43,36,46,33,42,32,44,40,49,35,48,47,26);(18,20,21,33,23,35,38,34,25,32,39,47,24,36,22,40)(19,26,27,31,29,43,37,46,30,42,28,44,41,49,45,48);(20,32)(26,42)(31,44)(33,47)(34,40)(35,36)(43,49)(46,48)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4990);