Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×#14519684 |
| Sylow | C61 ⋊ C4×#95 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D61 |
| commutator | C2×C61 | C43 |
| Frattini | C24 | C22×D61 |
| Fitting | C22×C42×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C22×C42 | D61 |
| hypocenter | C61 | C4×#95 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23×C4 ◁ C22×C42 | |
752 conjugacy classes of subgroups.
2000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29566544, #29566571, #29566573, … |
| maximal normal subgroup of | #29566544, #29566571, #29566573, … |
| maximal quotient of | #29567932, #29567933, C4×#16839516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2730);