Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#91881 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×A5 |
| commutator, hypocenter | SL(2,𝔽5) | C23 |
| Frattini, cosocle | C2 | C23×A5 |
| Fitting, hypercenter | C2×D4 | A5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
357 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | #14514932, #14514935, #14514936, … |
| maximal normal subgroup of | #14514932, #14514935, #14514936, … |
| maximal quotient of | C2×#11751534, C2×#11751539, C4×#91881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10887);