Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C109 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#89137 |
| commutator, socle | C2×C109 | C23×C4 |
| Fitting | C2×D4×C109 | C4 |
| hypercenter | C2×D4 | #89137 |
| hypocenter | C109 | #568 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
258 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,e^2=f,d^a=df,g^a=g^33,c^b=cf,g^e=g^108304 conjugacy classes — view the full character table.
| maximal subgroup of | #28378989, #28379004, #28379033, … |
| maximal normal subgroup of | #28378989, #28379004, #28379033, … |
| maximal quotient of | #28379596, #28379598, #28379603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1627);