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,g^a=g^108,d^b=de1105 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28362127, #28362131, #28362189, … |
| maximal normal subgroup of | #28362127, #28362131, #28362189, … |
| maximal quotient of | Q8×C4⋊Dic109, #28365950, #28365987, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1278);