Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C61×#405 ⋊ C2 |
| Sylow | C61 ⋊ #3175 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D244 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#405 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #405 | D61 |
| hypocenter | C61 | #3175 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
362 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^60,d^b=dg1232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29835121, #29835123, #29835166, … |
| maximal normal subgroup of | #29835121, #29835123, #29835166, … |
| maximal quotient of | #29680585, #29684286, #29684294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 15149);