Finite Group DatabasebetaFinite Group Databasebeta| order | 3840 |
| isoclinism | isoclinic class of #14515304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| direct product | C2×#14515304 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11757163 |
| commutator, hypocenter | #14515304 | C2 |
| Frattini | C2 | C2×#11757163 |
| Fitting, socle | C26 | A5 |
| cosocle | C25 | C2×A5 |
| LCS | G ▷ #14515304 | |
| UCS | C1 ◁ C22 | |
507 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 507 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
44 conjugacy classes — view the full character table.
| maximal subgroup of | #72209937, #72266551, #72266628, … |
| maximal quotient of | #72227889 |
Past the SmallGroups library coverage — no SmallGroups id.