Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #1020⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | C2×#1020⋊D5 |
| Fitting | C25×C5 ⋊ C2×D3 |
| derived | C5×C22⋊A4 ⋊ C23 |
| Sylow | C5 ⋊ C2×#1020⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #1020⋊D5 |
| commutator, cosocle, hypocenter | C5×C22⋊A4 | C23 |
| Frattini | C22 | C2×D5×S4 |
| Fitting | C25×C5 | C2×D3 |
| socle | C23×C5 | C2×S4 |
| LCS | G ▷ C5×C22⋊A4 | |
| UCS | C1 ◁ C2 | |
926 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×#1020⋊C2, #72243403, #72243405, … |
| maximal normal subgroup of | C2×D5×#1020⋊C2, #72243403, #72243405, … |
| maximal quotient of | #72243403, #72243415 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239370);