Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| isoclinism | isoclinic class of Dic122 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×C8×Dic122 |
| Sylow | C61 ⋊ C2×C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D61 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C2×C4×C8×C61 | C2 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C4×C8 | D61 |
| hypocenter | C61 | C2×C8×Q8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C8 ◁ C2×C4×C8 | |
440 conjugacy classes of subgroups.
2000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14519695, #29570587, C8×#14519702, … |
| maximal normal subgroup of | C8×#14519695, #29570587, C8×#14519702, … |
| maximal quotient of | C2×C8×C4⋊Dic61, C2×C8×#11758196, C4×C8×Dic122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13431);