Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D4×#6732 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×A5 |
| commutator | C2×SL(2,𝔽5) | C23 |
| Frattini, socle, cosocle | C22 | C23×A5 |
| Fitting, hypercenter | C4×D4 | A5 |
| hypocenter | SL(2,𝔽5) | C2×D4 |
| LCS | G ▷ C2×SL(2,𝔽5) ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
804 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D4×GL(2,𝔽5), S4×#6732, SD16×#6732, … |
| maximal normal subgroup of | D4×GL(2,𝔽5), SD16×#6732, #72276971 |
| maximal quotient of | SD16×#6732 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240869);