Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C24 |
| direct product | C2×C5×#1020 |
| Fitting, socle | C25×C5 ⋊ D3 |
| derived | C22⋊A4 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #1020 |
| commutator, cosocle, hypocenter | C22⋊A4 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C25×C5 | D3 |
| LCS | G ▷ C22⋊A4 | |
| UCS | C1 ◁ C2×C5 | |
476 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#1020⋊C4, C5×#72991, C5×#73081, … |
| maximal normal subgroup of | C5×#1020⋊C4, C5×#72991, C5×#73081, … |
| maximal quotient of | C5×#87502, C4×C5×#1020, C5×C4⋊#1020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11380);