Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #135×#6923 |
| Fitting | #135×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×#135 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×#6923 |
| commutator | C4×C61 | C23×C4 |
| Frattini | C4 | C23×#6923 |
| Fitting | #135×C61 | C4 |
| socle | C2×C61 | C2×C4×D4 |
| hypercenter | #135 | #6923 |
| hypocenter | C61 | C4×#135 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #135 | |
500 conjugacy classes of subgroups.
266 conjugacy classes — view the full character table.
| maximal subgroup of | #359×#6923, #30606598, #360×#6923, … |
| maximal normal subgroup of | #359×#6923, #30606598, #360×#6923, … |
| maximal quotient of | #135×#92420, #30612279, #30612280, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21260);