Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C8×C109 ⋊ C2 |
| Sylow | C109 ⋊ #436 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D109 |
| commutator, socle | C22×C109 | C22×C4 |
| Fitting | C22⋊C8×C109 | C2 |
| hypercenter | C22⋊C8 | D109 |
| hypocenter | C109 | #436 |
| LCS | G ▷ C22×C109 ▷ C109 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,109|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,c^b=cf,g^c=g^1081108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #436×D109, C2×#20295101, #28371730, … |
| maximal normal subgroup of | #436×D109, C2×#20295101, #28371730, … |
| maximal quotient of | #28361914, #28361919, #28361925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 624);