Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #2276 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator | C2×C61 | C22×C42 |
| Fitting | C2×C4×Q8×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C2×C4×Q8 | D61 |
| hypocenter | C61 | #2276 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
628 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 389 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=f,b^2=g,c^2=ef,d^2=e,b^a=be,d^a=de,c^b=ce,h^b=h^601268 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29576913, #29576917, #29576927, … |
| maximal normal subgroup of | #29576913, #29576917, #29576927, … |
| maximal quotient of | #29601098, #29601302, #29601306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6875);