Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C23×Q8×D61 |
| Fitting | C23×Q8×C61 ⋊ C2 |
| Sylow | C61 ⋊ C24×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D61 |
| commutator | C2×C61 | C26 |
| Frattini | C2 | C25×D61 |
| Fitting | C23×Q8×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C23×Q8 | D61 |
| hypocenter | C61 | C24×Q8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C23×Q8 | |
6264 conjugacy classes of subgroups.
1280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×#1446, #29602397, #29602400, … |
| maximal normal subgroup of | D61×#1446, #29602397, #29602400, … |
| maximal quotient of | C23×C4⋊C4×D61, C22×C4×Q8×D61, C23×#14519742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19304);