Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #1797 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator | C22×C61 | C22×C8 |
| Fitting | C22×C42×C61 | C2 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C22×C42 | D61 |
| hypocenter | C61 | #1797 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C42 | |
400 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,b^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^601976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29566550, #29566551, #29566562, … |
| maximal normal subgroup of | #29566550, #29566551, #29566562, … |
| maximal quotient of | #29572670, #29572674, #29572678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4490);