Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C109 ⋊ #407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D109 |
| commutator, socle | C22×C109 | C22×C4 |
| Fitting | C23×C4×C109 | C2 |
| hypercenter | C23×C4 | D109 |
| hypocenter | C109 | #407 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 | |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^1081756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28360884, #28360885, #28360908, … |
| maximal normal subgroup of | #28360884, #28360885, #28360908, … |
| maximal quotient of | #28361359, #28361362, #28361366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 513);