Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C109 ⋊ #408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#89137 |
| commutator, socle | C22×C109 | C22×C4 |
| Fitting | C2×Q8×C109 | C4 |
| hypercenter | C2×Q8 | #89137 |
| hypocenter | C109 | #408 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,e^2=f,b^a=bd,g^a=g^33,c^b=cf,g^b=g^108,g^c=g^108,g^e=g^108298 conjugacy classes — view the full character table.
| maximal subgroup of | #28378134, #28378881, #28378990, … |
| maximal normal subgroup of | #28378134, #28378881, #28378990, … |
| maximal quotient of | #28378300, #28378303, #28378306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1524);