Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#17984820 |
| Fitting | C2×C4⋊C4×C139 ⋊ C2 |
| Sylow | C139 ⋊ C2×C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D139 |
| commutator | C22×C139 | C24 |
| Frattini | C22 | C23×D139 |
| Fitting | C2×C4⋊C4×C139 | C2 |
| socle | C23×C139 | C23 |
| hypercenter | C2×C4⋊C4 | D139 |
| hypocenter | C139 | C2×C22⋊Q8 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
322 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31804766, C4×#17984820, #31808938, … |
| maximal normal subgroup of | #31804766, C4×#17984820, #31808938, … |
| maximal quotient of | C2×#22580812, C2×#22580824, C2×#22580827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 1046);