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×#454 |
| 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 | |
146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(2,6)(4,11)(7,15)(8,12)(9,13)(14,16)(17,18,19,20,21);(1,2)(3,7)(4,12)(5,8)(6,11)(9,14)(10,16)(13,15);(1,3,5,10)(2,7,8,16)(4,13,11,9)(6,14,12,15)80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 955);