Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Sylow | C61 ⋊ #2862 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator, socle | C23×C61 | C24 |
| Fitting | C43×C61 | C2 |
| hypercenter | C43 | D61 |
| hypocenter | C61 | #2862 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C43 | |
504 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^601964 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29568381, #29568383, #29568473, … |
| maximal normal subgroup of | #29568381, #29568383, #29568473, … |
| maximal quotient of | #29611205, #29611314, #29611350, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 12888);