Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C139 ⋊ #441 |
| 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 | #441 |
| LCS | G ▷ C4×C139 ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,139|a^2=e,b^2=f,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 | #31808295, #31808297, #441×D139, … |
| maximal normal subgroup of | #31808295, #31808297, #441×D139, … |
| maximal quotient of | #31805224, #31805277, #31805314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 657);