Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C61 ⋊ #2677 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator, socle | C23×C61 | C24 |
| Fitting | C2×C22⋊Q8×C61 | C2 |
| hypercenter | C2×C22⋊Q8 | D61 |
| hypocenter | C61 | #2677 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
544 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,b^2=e,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | #29886821, #29886825, #29886827, … |
| maximal normal subgroup of | #29886821, #29886825, #29886827, … |
| maximal quotient of | #29607360, #29607364, #29607942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 10821);