Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C61×#336 ⋊ C2 |
| Sylow | C61 ⋊ C8×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator | C2×C61 | C2×C4×C8 |
| Fitting | C61×#336 | C2 |
| socle | C23×C61 | C22×C4 |
| hypercenter | #336 | D61 |
| hypocenter | C61 | C8×C22⋊C4 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=e,b^2=f,c^2=e,e^2=g,b^a=bd,h^c=h^601280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×C22⋊C4×D61, C2×#21445589, #29677600, … |
| maximal normal subgroup of | C8×C22⋊C4×D61, C2×#21445589, #29677600, … |
| maximal quotient of | #29570477, #29570485, #29570500, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4280);