Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #14515300 |
| automorphism | Aut(G) = #72240859 (order 7680) · Inn(G) = #11757162 · Out(G) = D4 |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C25 ⋊ A5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2 | #11757162 |
| commutator, hypocenter | G | C1 |
| Fitting, cosocle | C25 | A5 |
| LCS | G | |
| UCS | C1 ◁ C2 | |
219 conjugacy classes of subgroups; only the 4 normal subgroups are shown.
This group has 219 conjugacy classes of subgroups — too many to draw. Only its 4 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 12 |
| transitive degree | μt(G) = 12 |
A minimal faithful permutation representation — 2 generators on 12 points:
(1,12,2,6,3,4,10,5,9,7)(8,11);(1,4)(2,10,3,9,8,5,12,7,6,11)16 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240998);