Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C2×#124×C61 ⋊ C2 |
| Sylow | C61 ⋊ #2733 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator, socle | C23×C61 | C24 |
| Fitting | C2×#124×C61 | C2 |
| hypercenter | C2×#124 | D61 |
| hypocenter | C61 | #2733 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
592 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 137 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=ef,b^2=f,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^c=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | #29599040, #29599042, #29599472, … |
| maximal normal subgroup of | #29599040, #29599042, #29599472, … |
| maximal quotient of | #29607901, #29607903, #29608474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 11534);