Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C241 ⋊ #106 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D964 |
| commutator | C4×C241 | C2×C4 |
| Frattini | C2×C4 | C2×D241 |
| Fitting | C2×C8×C241 | C2 |
| socle | C22×C241 | D4 |
| hypercenter | C2×C8 | D241 |
| hypocenter | C241 | #106 |
| LCS | G ▷ C4×C241 ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,241|a^2=d,b^2=c,c^2=e,b^a=bc,c^a=ce,f^a=f^2401934 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29507527, #29507528, #29507540, … |
| maximal normal subgroup of | #29507527, #29507528, #29507540, … |
| maximal quotient of | #29507468, #29507480, #29507540, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 78);