Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4×D15 |
| Fitting | C23×C3×C4×C5 ⋊ C2 |
| derived, Hall | C3×C5 ⋊ C24×C4 |
| Sylow | C5 ⋊ C23×C4×D3 |
| Sylow | C3 ⋊ C23×C4×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D15 |
| commutator, hypocenter | C3×C5 | C24×C4 |
| Frattini | C2 | C24×D15 |
| Fitting | C23×C3×C4×C5 | C2 |
| socle | C24×C3×C5 | C22 |
| prime radical | C24×D15 | C2 |
| cosocle | C2×C3×C5 | C25 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C23×C4 | |
2724 conjugacy classes of subgroups; only the 1035 normal subgroups are shown.
This group has 2724 conjugacy classes of subgroups — too many to draw. Only its 1035 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14279858, #14279873, #14296793, … |
| maximal normal subgroup of | #14279858, #14279873, #14296793, … |
| maximal quotient of | C22×C42×D15, C23×C4×Dic15, C22×C22⋊C4×D15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11329);