Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C61 ⋊ #1726 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator | C2×C61 | C43 |
| Fitting | C2×#97×C61 | C2 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×#97 | D61 |
| hypocenter | C61 | #1726 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#97 | |
328 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 205 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,c^2=f,d^2=g,h^a=h^60,c^b=cg,h^c=h^601280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29570453, #29570457, #29570461, … |
| maximal normal subgroup of | #29570453, #29570457, #29570461, … |
| maximal quotient of | #97×#92418, #29569365, #29569370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4198);