Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×D4×#6923 |
| Fitting | C4×D4×C61 ⋊ C4 |
| Sylow | C61 ⋊ C42×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6923 |
| commutator | C2×C61 | C22×C42 |
| Frattini | C22 | C23×#6923 |
| Fitting | C4×D4×C61 | C4 |
| socle | C22×C61 | C23×C4 |
| hypercenter | C4×D4 | #6923 |
| hypocenter | C61 | C42×D4 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
924 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊C8×#6923, #30597551, #30597557, … |
| maximal normal subgroup of | D4⋊C8×#6923, #30597551, #30597557, … |
| maximal quotient of | C4×C22⋊C4×#6923, C4×C4⋊C4×#6923, C4×#16840710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20944);