Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C4×Dic137 |
| Sylow | C137 ⋊ C4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D137 |
| commutator | C2×C137 | C2×C42 |
| Fitting | C2×C22⋊C4×C137 | C2 |
| socle | C23×C137 | C23 |
| hypercenter | C2×C22⋊C4 | D137 |
| hypocenter | C137 | C4×C22⋊C4 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31780576, #99×Dic137, #31781623, … |
| maximal normal subgroup of | #31780576, #99×Dic137, #31781623, … |
| maximal quotient of | #95×Dic137, #31779011, #31779014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 399);