Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C109 ⋊ C2 |
| Sylow | C109 ⋊ #431 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D109 |
| commutator | C2×C109 | C22×C8 |
| Frattini | C2×C4 | C22×D109 |
| Fitting | C4×C8×C109 | C2 |
| socle | C22×C109 | C22×C4 |
| hypercenter | C4×C8 | D109 |
| hypocenter | C109 | #431 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^1081768 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#13182012, #28361311, #28361314, … |
| maximal normal subgroup of | C8×#13182012, #28361311, #28361314, … |
| maximal quotient of | #28362777, C4×#16812611, C4×#16812628, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 600);