Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12952 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12953 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1864 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C22×D8×C17 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
416 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)(18,19,22,28,24,29,23,41)(20,30,33,45,35,42,34,49)(21,36,38,46,40,26,39,27)(25,37,43,31,44,48,47,32);(18,20)(19,25,29,44)(21,37)(22,34)(23,33)(24,35)(26,42,36,30)(27,45,46,49)(28,47,41,43)(31,39)(32,38)(40,48);(19,26)(21,38)(22,23)(25,42)(27,41)(28,46)(29,36)(30,44)(31,48)(32,37)(33,34)(39,40)(43,45)(47,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5941);