Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #2873 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D61 |
| commutator | C2×C61 | C22×C42 |
| Fitting | C22×M16×C61 | C2 |
| socle | C22×C61 | C23×C4 |
| hypercenter | C22×M16 | D61 |
| hypocenter | C61 | #2873 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C22×M16 | |
564 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,b^2=f,e^2=g,d^a=dg,c^b=cg,h^b=h^601268 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29585689, #29585690, #29585693, … |
| maximal normal subgroup of | #29585689, #29585690, #29585693, … |
| maximal quotient of | #29645596, #29645597, #29645620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 12928);