Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D139)⋊C8 |
| Fitting | C22⋊C8×C139 ⋊ C2 |
| Sylow | C139 ⋊ C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D139 |
| commutator | C2×C139 | C22×C8 |
| Fitting | C22⋊C8×C139 | C2 |
| socle | C22×C139 | C22×C4 |
| hypercenter | C22⋊C8 | D139 |
| hypocenter | C139 | C8×D4 |
| LCS | G ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
134 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,139|a^2=e,c^2=e,e^2=f,b^a=bd,g^c=g^1381420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D4×D139, C2×(C22⋊D139)⋊C8, #31815094, … |
| maximal normal subgroup of | C8×D4×D139, C2×(C22⋊D139)⋊C8, #31815094, … |
| maximal quotient of | #31805196, #31805201, #31805207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 612);