Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #2971 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | C4×Q8×C61 | C4 |
| hypercenter | C4×Q8 | #6923 |
| hypocenter | C61 | #2971 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
402 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 168 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=f,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=dg,h^a=h^11,c^b=cg,h^b=h^60,d^c=dg,h^c=h^11,h^f=h^60350 conjugacy classes — view the full character table.
| maximal subgroup of | #30600441, #30600443, #30600449, … |
| maximal normal subgroup of | #30600441, #30600443, #30600449, … |
| maximal quotient of | #30614413, #30614486, Q8×#14519832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21354);