Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C61 ⋊ #3028 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#14519746 |
| commutator | C23×C61 | C24 |
| Frattini | C23 | C23×D61 |
| Fitting | C61×#585 | C2 |
| socle | C2×C61 | C2×#120 |
| hypercenter | #585 | D61 |
| hypocenter | C61 | #3028 |
| LCS | G ▷ C23×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #585 | |
716 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 161 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=g,d^2=g,b^a=be,c^a=cf,d^a=dg,h^a=h^60,f^b=fg,e^c=eg1049 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29599003, #29599004, #29599007, … |
| maximal normal subgroup of | #29599003, #29599004, #29599007, … |
| maximal quotient of | #29654052, #29654059, #29654066, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 13916);