Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C109 ⋊ C4 |
| Sylow | C109 ⋊ #443 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#89137 |
| commutator | C4×C109 | C22×C4 |
| Frattini | C4 | C22×#89137 |
| Fitting | Q16×C109 | C4 |
| socle | C2×C109 | C4×D4 |
| hypercenter | Q16 | #89137 |
| hypocenter | C109 | #443 |
| LCS | G ▷ C4×C109 ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^76,d^b=df,g^b=g^108,g^c=g^33,g^e=g^108217 conjugacy classes — view the full character table.
| maximal subgroup of | #28379432, #28379433, #28379434, … |
| maximal normal subgroup of | #28379432, #28379433, #28379434, … |
| maximal quotient of | #28378613, #28378616, Q16×#11724786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1593);