Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #87588 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C26 |
| direct product | C5×#87588 |
| Fitting, socle | C26×C5 ⋊ D3 |
| derived | C22⋊(C22⋊A4) ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #87588 |
| commutator, cosocle, hypocenter | C22⋊(C22⋊A4) | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C26×C5 | D3 |
| LCS | G ▷ C22⋊(C22⋊A4) | |
| UCS | C1 ◁ C5 | |
1660 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,3,4,5)(8,9)(10,12)(14,17,16,15);(7,8,9)(11,12,13)(15,16,17);(6,9)(7,8)120 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#87588 |
| maximal normal subgroup of | D5×#87588 |
| maximal quotient of | C5×#11715850 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237186);