Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #11757163 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C22 |
| direct product | C2×#11757163 |
| Fitting, socle | C25 ⋊ A5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11757163 |
| commutator, hypocenter | #11757163 | C2 |
| Frattini | C1 | G |
| Fitting, socle | C25 | A5 |
| cosocle | C24 | C2×A5 |
| LCS | G ▷ #11757163 | |
| UCS | C1 ◁ C2 | |
245 conjugacy classes of subgroups; only the 6 normal subgroups are shown.
This group has 245 conjugacy classes of subgroups — too many to draw. Only its 6 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10 |
24 conjugacy classes — view the full character table.
| maximal subgroup of | #72209666, #72210099, #72218849, … |
| maximal normal subgroup of | C2×#11757163⋊C2, C2×C3×#11757163, C22×#11757163, … |
| maximal quotient of | #72209926, #72209930, C2×#14515304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240997);