Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#453 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | #120 |
| commutator, Frattini, cosocle | C2×C4 | C23×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C4×C5 ◁ G | |
168 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 3 generators on 13 points:
(2,5)(3,7)(6,8)(9,10,11,12,13);(1,2)(3,8)(4,6)(5,7);(3,7)(5,8)80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 954);