Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×C22⋊#6923 |
| Fitting | C22×Q8×C61 ⋊ C4 |
| Sylow | C61 ⋊ Q8×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C22×Q8×C61 | C4 |
| hypercenter | C22×Q8 | #6923 |
| hypocenter | C61 | Q8×C22⋊C4 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
820 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 228 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
350 conjugacy classes — view the full character table.
| maximal subgroup of | #30600683, #30600684, #30600691, … |
| maximal normal subgroup of | #30600683, #30600684, #30600691, … |
| maximal quotient of | C4⋊C4×C22⋊#6923, Q8×(C2×#6923)⋊C4, #30608743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21014);