Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D15×H(5,𝔽2) |
| Fitting | C3×C5×H(5,𝔽2) ⋊ C2 |
| Hall | C3×C5 ⋊ C2×H(5,𝔽2) |
| Sylow | C5 ⋊ D3×H(5,𝔽2) |
| Sylow | C3 ⋊ D5×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D15 |
| commutator, socle, cosocle | C2×C3×C5 | C25 |
| Fitting | C3×C5×H(5,𝔽2) | C2 |
| hypercenter | H(5,𝔽2) | D15 |
| hypocenter | C3×C5 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
1796 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 1796 conjugacy classes of subgroups — too many to draw. Only its 581 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#453, #14424982, D15×#455, … |
| maximal normal subgroup of | D15×#453, #14424982, D15×#455, … |
| maximal quotient of | D15×#518, D15×#520, #14479194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11342);