Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1281 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #11758198 |
| commutator | C22×C61 | C4×C8 |
| Frattini | C2×C42 | C2×D61 |
| Fitting | C61×#431 | C2 |
| socle | C22×C61 | #95 |
| hypercenter | #431 | D61 |
| hypocenter | C61 | #1281 |
| LCS | G ▷ C22×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 ◁ #431 | |
152 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=d,b^2=e,d^2=g,e^2=f,b^a=bc,c^a=cf,d^b=df,h^b=h^601244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×#1281, C2×#21443663, #29569642, … |
| maximal normal subgroup of | D61×#1281, C2×#21443663, #29569642, … |
| maximal quotient of | #29566542, #29566546, #29566548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2354);