Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #392⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#392⋊C3 |
| unambiguous semidirect product | #392⋊(C3×C5) |
| unambiguous semidirect product | (C5×#392)⋊C3 |
| Fitting, Hall | C5×#392 ⋊ C3 |
| Sylow | #392 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #127⋊C3 |
| commutator, cosocle, hypocenter | #95 | C2×C3×C5 |
| Frattini | C23 | C2×C5×A4 |
| Fitting | C5×#392 | C3 |
| socle | C23×C5 | C2×A4 |
| LCS | G ▷ #95 | |
| UCS | C1 ◁ C2×C5 | |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3,4,5)(6,11,16,9,8,15,10,13,12,7,14,17);(6,9,10,7)(11,13)(12,15)(16,17)90 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#68000, C5×#72995, C5×#72996, … |
| maximal normal subgroup of | C5×#68000, C5×#72995, C5×#72996, … |
| maximal quotient of | C5×#1444⋊C3, C5×#2017⋊C3, C2×C5×#392⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3727);