Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1452 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator, socle | C22×C61 | C2×C42 |
| Fitting | C4×C8×C61 | C4 |
| hypercenter | C4×C8 | #6923 |
| hypocenter | C61 | #1452 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×C8 | |
196 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bg,c^b=cf,h^b=h^11,h^c=h^60,h^e=h^60536 conjugacy classes — view the full character table.
| maximal subgroup of | #30594206, #30594209, #30597395, … |
| maximal normal subgroup of | #30594206, #30594209, #30597395, … |
| maximal quotient of | #30595969, #30595991, #30597380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19724);