Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #97×C139 ⋊ C2 |
| Sylow | C139 ⋊ #440 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D556 |
| commutator | C4×C139 | C22×C4 |
| Frattini | C2×C4 | C22×D139 |
| Fitting | #97×C139 | C2 |
| socle | C22×C139 | C2×D4 |
| hypercenter | #97 | D139 |
| hypocenter | C139 | #440 |
| LCS | G ▷ C4×C139 ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^138,d^b=df,g^b=g^1381402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #440×D139, C2×#22581055, #31815199, … |
| maximal normal subgroup of | #440×D139, C2×#22581055, #31815199, … |
| maximal quotient of | #31805218, #31805263, #31805284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 651);