Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #2153 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×D244 |
| commutator | C4×C61 | C22×C8 |
| Frattini | C2×C8 | C22×D61 |
| Fitting | C61×#405 | C2 |
| socle | C2×C61 | C2×C4⋊C8 |
| hypercenter | #405 | D61 |
| hypocenter | C61 | #2153 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ C22×C8 ◁ #405 | |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^60,c^b=cg1244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29591530, #29591531, #29591535, … |
| maximal normal subgroup of | #29591530, #29591531, #29591535, … |
| maximal quotient of | #29591561, #29591587, #29591621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6276);