Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1436 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D61 |
| commutator | C22×C61 | C2×C42 |
| Fitting | C22×C42×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C22×C42 | D61 |
| hypocenter | C61 | #1436 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
612 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,b^2=g,c^2=f,b^a=bd,c^a=ce,h^a=h^601976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29571530, D61×#1436, C2×#21444052, … |
| maximal normal subgroup of | #29571530, D61×#1436, C2×#21444052, … |
| maximal quotient of | #29567933, #29567938, #29567939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2743);