Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D109⋊#131 |
| Sylow | C109 ⋊ C2×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#89137 |
| commutator, socle | C2×C109 | C23×C4 |
| Frattini | C2 | C23×#89137 |
| Fitting | #41×C109 | C4 |
| hypercenter | #41 | #89137 |
| hypocenter | C109 | C2×#131 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C4 ◁ #41 | |
266 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,e^2=f,g^a=g^33,c^b=cf,g^d=g^108,g^e=g^108310 conjugacy classes — view the full character table.
| maximal subgroup of | #28378808, #28378812, #28379071, … |
| maximal normal subgroup of | #28378808, #28378812, #28379071, … |
| maximal quotient of | #28379592, C4×#16812786, C4×#16812787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1625);