Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×C22⋊D137 |
| Fitting | C22×C8×C137 ⋊ C2 |
| Sylow | C137 ⋊ C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×D137 |
| commutator | C2×C137 | C22×C8 |
| Frattini | C2×C4 | C22×D137 |
| Fitting | C22×C8×C137 | C2 |
| socle | C22×C137 | C22×C4 |
| hypercenter | C22×C8 | D137 |
| hypocenter | C137 | C8×D4 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
134 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31782606, C16×C22⋊D137, #31782611, … |
| maximal normal subgroup of | #31782606, C16×C22⋊D137, #31782611, … |
| maximal quotient of | C8×#14555495, C8×#14555498, C8×#14555497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 613);