Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C109 ⋊ C4 |
| Sylow | C109 ⋊ #520 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#89137 |
| commutator, socle | C2×C109 | C23×C4 |
| Fitting | #41×C109 | C4 |
| hypercenter | #41 | #89137 |
| hypocenter | C109 | #520 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2 ◁ #41 | |
294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 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=f,d^2=e,b^a=be,d^a=de,g^a=g^33,c^b=ce,g^f=g^108304 conjugacy classes — view the full character table.
| maximal subgroup of | #28378991, #28378992, #28379031, … |
| maximal normal subgroup of | #28378991, #28378992, #28379031, … |
| maximal quotient of | #28379469, #28379471, #28379472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1618);