Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | Q8×#11758187 |
| Sylow | C61 ⋊ Q8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C22×C16 |
| Fitting | C4×Q8×C61 | C4 |
| socle | C22×C61 | C22×C8 |
| hypercenter | C4×Q8 | #6923 |
| hypocenter | C61 | Q8×C16 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
134 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#11758187, #30605913, #30605919, … |
| maximal normal subgroup of | SD16×#11758187, #30605913, #30605919, … |
| maximal quotient of | C4⋊C4×#11758187, #30607765, #30607893, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20923);