Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#5431 |
| Fitting | C5×2−1+4 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | GL(2,ℤ/4) |
| commutator, cosocle | #41⋊C3 | C22×C5 |
| Frattini | C4 | C2×C5×S4 |
| Fitting | C5×2−1+4 | D3 |
| hypercenter | C5×D4 | S4 |
| hypocenter | SL(2,𝔽3) | C5×D4 |
| LCS | G ▷ #41⋊C3 ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C2×C5 ◁ C4×C5 ◁ C5×D4 | |
144 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
85 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#85470, C5×#85472, C5×#85473, … |
| maximal normal subgroup of | C5×#85470, C5×#85472, C5×#85473, … |
| maximal quotient of | C5×#73075, C5×#73078, C5×#73086, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6297);