Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×B(4,𝔽2)⋊C3 |
| unambiguous semidirect product | B(4,𝔽2)⋊(C3×C5) |
| unambiguous semidirect product | (C5×B(4,𝔽2))⋊C3 |
| Fitting, Hall | C5×B(4,𝔽2) ⋊ C3 |
| derived | H(5,𝔽2) ⋊ C2×C3×C5 |
| Sylow | B(4,𝔽2) ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C5 | #120⋊C3 |
| commutator, cosocle, hypocenter | H(5,𝔽2) | C2×C3×C5 |
| Frattini | C23 | C2×C5×A4 |
| Fitting | C5×B(4,𝔽2) | C3 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C2×C5 | |
116 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,2,3,4,5)(7,12,11,10,8,13);(6,11)(7,8)(9,13)(10,12)80 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#73025, C5×#73026, C5×#73027, … |
| maximal normal subgroup of | C5×#73025, C5×#73026, C5×#73027, … |
| maximal quotient of | C5×#1790⋊C3, C5×#2029⋊C3, C5×#2062⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3734);