Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C139 ⋊ C2 |
| Sylow | C139 ⋊ #556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D139 |
| commutator, socle | C22×C139 | C24 |
| Fitting | C22⋊Q8×C139 | C2 |
| hypercenter | C22⋊Q8 | D139 |
| hypocenter | C139 | #556 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,139|b^2=ef,c^2=e,d^2=e,b^a=be,c^a=cf,d^b=de,g^b=g^138,g^c=g^138991 conjugacy classes — view the full character table.
| maximal subgroup of | #31818314, #31818316, #31818336, … |
| maximal normal subgroup of | #31818314, #31818316, #31818336, … |
| maximal quotient of | #31809296, #31809299, #31809348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 1270);