Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#41×C61 ⋊ C4 |
| Sylow | C61 ⋊ #3428 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C23×#6923 |
| commutator, socle | C2×C61 | C24×C4 |
| Frattini | C2 | C24×#6923 |
| Fitting | C2×#41×C61 | C4 |
| hypercenter | C2×#41 | #6923 |
| hypocenter | C61 | #3428 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
1540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,e^2=f,b^a=bf,d^a=df,h^a=h^11,c^b=cf,h^g=h^60368 conjugacy classes — view the full character table.
| maximal subgroup of | #30602446, #30602449, #30602460, … |
| maximal normal subgroup of | #30602446, #30602449, #30602460, … |
| maximal quotient of | #30624549, #30624552, C4×#16840829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21490);