Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×#95×C61 ⋊ C2 |
| Sylow | C61 ⋊ #1438 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D61 |
| commutator | C23×C61 | C22×C4 |
| Fitting | C2×#95×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C2×#95 | D61 |
| hypocenter | C61 | #1438 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
1168 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 209 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=g,b^a=bd,c^a=ce,c^b=cf,h^b=h^60,h^c=h^601244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29566758, #29572139, #29575148, … |
| maximal normal subgroup of | #29566758, #29572139, #29575148, … |
| maximal quotient of | #29567934, #29567941, #29586500, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2750);