Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33963 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#2246 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×Q8×C17 ◁ C8×Q8×C17 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(24,25)(26,27,32,36)(28,33,31,46)(29,39,41,56)(30,42,45,55)(34,49,51,40)(35,38,53,44)(37,54,47,52)(43,48,57,50);(18,19,22,23)(20,24,21,25)(26,28,32,31)(27,33,36,46)(29,37,41,47)(30,38,45,44)(34,48,51,50)(35,42,53,55)(39,54,56,52)(40,43,49,57);(18,20,22,21)(19,24,23,25)(26,29,32,41)(27,34,36,51)(28,37,31,47)(30,43,45,57)(33,48,46,50)(35,52,53,54)(38,49,44,40)(39,55,56,42);(18,21,22,20)(19,24,23,25)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26951);