Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C109 ⋊ #340 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D436 |
| commutator | C4×C109 | C42 |
| Frattini | C22×C4 | C2×D109 |
| Fitting | C22×C8×C109 | C2 |
| socle | C23×C109 | D4 |
| hypercenter | C22×C8 | D109 |
| hypocenter | C109 | #340 |
| LCS | G ▷ C4×C109 ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,109|a^2=d,b^2=e,c^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^1081756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28361041, #28361042, #28361044, … |
| maximal normal subgroup of | #28361041, #28361042, #28361044, … |
| maximal quotient of | #28360867, #28360872, #28360891, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 312);