Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| isoclinism | isoclinic class of Dic122 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C24×Dic122 |
| Sylow | C61 ⋊ C24×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D61 |
| commutator | C2×C61 | C26 |
| Frattini | C2 | C25×D61 |
| Fitting | C24×C4×C61 | C2 |
| socle | C25×C61 | C22 |
| hypercenter | C24×C4 | D61 |
| hypocenter | C61 | C24×Q8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
6264 conjugacy classes of subgroups.
2000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#21444089, #29602398, #29602399, … |
| maximal normal subgroup of | C2×#21444089, #29602398, #29602399, … |
| maximal quotient of | C24×#11758196, C24×C4⋊Dic61, C23×C4×Dic122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19305);