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×#33931 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C2×D8×C17 | C23 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×Q8×C17 ◁ C8×Q8×C17 ◁ G | |
472 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)(19,22)(23,24)(26,27)(28,33)(29,39)(30,42)(31,46)(32,36)(34,40)(35,44)(37,53)(38,52)(41,56)(43,48)(45,55)(47,51)(49,57)(50,54);(18,19,21,22)(20,24,25,23)(26,28,32,31)(27,33,36,46)(29,37,41,47)(30,38,45,44)(34,48,50,49)(35,42,52,55)(39,53,56,51)(40,43,54,57);(26,29,32,41)(27,34,36,50)(28,37,31,47)(30,43,45,57)(33,48,46,49)(35,51,52,53)(38,54,44,40)(39,55,56,42);(18,20,21,25)(19,23,22,24)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26919);