Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #95×C139 ⋊ C2 |
| Sylow | C139 ⋊ #385 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D139 |
| commutator | C22×C139 | C22×C4 |
| Fitting | #95×C139 | C2 |
| socle | C23×C139 | C23 |
| hypercenter | #95 | D139 |
| hypocenter | C139 | #385 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C23 ◁ #95 | |
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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=f,b^2=f,b^a=bd,c^a=ce,g^a=g^138,g^c=g^1381408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #385×D139, C2×#22580827, #31808842, … |
| maximal normal subgroup of | #385×D139, C2×#22580827, #31808842, … |
| maximal quotient of | (C2×D139)⋊#95, #31804638, #31804639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 423);