Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C109 ⋊ #557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D109 |
| commutator, socle | C22×C109 | C24 |
| Fitting | C4⋊Q8×C109 | C2 |
| hypercenter | C4⋊Q8 | D109 |
| hypocenter | C109 | #557 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
200 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=f,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,g^d=g^108781 conjugacy classes — view the full character table.
| maximal subgroup of | #28362125, #28362129, #28362187, … |
| maximal normal subgroup of | #28362125, #28362129, #28362187, … |
| maximal quotient of | #28365944, #28365951, #28365988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1274);