Finite Group DatabasebetaFinite Group Databasebeta| order | 2688 |
| isoclinism | isoclinic class of #13051525 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| direct product | C2×#13051525 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #13051525 |
| commutator, hypocenter | #13051525 | C2 |
| Frattini, cosocle | C23 | C2×GL(3,𝔽2) |
| Fitting, socle | C24 | GL(3,𝔽2) |
| LCS | G ▷ #13051525 | |
| UCS | C1 ◁ C2 | |
282 conjugacy classes of subgroups; only the 6 normal subgroups are shown.
This group has 282 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.
22 conjugacy classes — view the full character table.
| maximal subgroup of | #72209793, #72209820, #72209866, … |
| maximal normal subgroup of | C22×#13051525 |
| maximal quotient of | C2×#72209597, C22×#13051525 |
Past the SmallGroups library coverage — no SmallGroups id.