Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#11758185 |
| Sylow | C61 ⋊ C2×C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D61 |
| commutator | C2×C61 | C22×C16 |
| Frattini | C2×C8 | C22×D61 |
| Fitting | C2×C4×C8×C61 | C2 |
| socle | C23×C61 | C2×C8 |
| hypercenter | C2×C4×C8 | D61 |
| hypocenter | C61 | C2×C4⋊C16 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C8 ◁ C2×C4×C8 | |
184 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29566875, #29566876, #29566879, … |
| maximal normal subgroup of | #29566875, #29566876, #29566879, … |
| maximal quotient of | C2×#21443883, C2×#21443889, #29591613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6263);