Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #2295 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D61 |
| commutator | C22×C61 | C23×C4 |
| Frattini | C23 | C23×D61 |
| Fitting | C43×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C43 | D61 |
| hypocenter | C61 | #2295 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
500 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 229 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,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^601976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29567958, #29567961, #29568018, … |
| maximal normal subgroup of | #29567958, #29567961, #29568018, … |
| maximal quotient of | #29601124, #29601144, C4×#16839646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6987);