Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×C4×#11758226 |
| Fitting | C2×C4×Q8×C61 ⋊ C2 |
| Sylow | C61 ⋊ C2×C4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D61 |
| commutator | C2×C61 | C24×C4 |
| Frattini | C22 | C24×D61 |
| Fitting | C2×C4×Q8×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C2×C4×Q8 | D61 |
| hypocenter | C61 | C2×C4×#41 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×Q8 | |
1728 conjugacy classes of subgroups.
1280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29571388, #29645825, #29645883, … |
| maximal normal subgroup of | #29571388, #29645825, #29645883, … |
| maximal quotient of | C2×C4×#14519735, C2×C4×#14519739, C2×C4×Q8×Dic61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17691);