Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C109 ⋊ #364 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4⋊#89137 |
| commutator | C4×C109 | C2×C8 |
| Frattini | C2×C4 | C2×#89137 |
| Fitting | C42×C109 | C4 |
| socle | C2×C109 | C4⋊C8 |
| hypercenter | C42 | #89137 |
| hypocenter | C109 | #364 |
| LCS | G ▷ C4×C109 ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ C42 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^33,g^b=g^108,g^d=g^108460 conjugacy classes — view the full character table.
| maximal subgroup of | #28378040, #28378041, #28378042, … |
| maximal normal subgroup of | #28378040, #28378041, #28378042, … |
| maximal quotient of | #28378055, #28378062, #28378076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1472);