Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #6728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#91870 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2×C4 | S5 |
| commutator, cosocle, hypocenter | SL(2,𝔽5) | C23 |
| Frattini | C2 | C22×S5 |
| socle | C22 | C2×S5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C4 | |
262 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 24 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 | #14514937, C4×#91870, #14515067, … |
| maximal normal subgroup of | #14514937, C4×#91870, #14515067, … |
| maximal quotient of | C2×#11751515, C2×C4×#6729, C2×C4×#6728, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10867);