Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #1451 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D61 |
| commutator, socle | C22×C61 | C2×C42 |
| Fitting | C2×C4×C8×C61 | C2 |
| hypercenter | C2×C4×C8 | D61 |
| hypocenter | C61 | #1451 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C42 ◁ C2×C4×C8 | |
208 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 125 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=d,b^2=e,d^2=f,e^2=g,b^a=bg,c^a=cf,h^a=h^601976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29566906, #29566907, #29566912, … |
| maximal normal subgroup of | #29566906, #29566907, #29566912, … |
| maximal quotient of | #29569375, #29569395, #29570439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2799);