Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C241 ⋊ C2 |
| Sylow | C241 ⋊ C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D241 |
| commutator | C2×C241 | C2×C8 |
| Fitting | C2×C8×C241 | C2 |
| socle | C22×C241 | C2×C4 |
| hypercenter | C2×C8 | D241 |
| hypocenter | C241 | C22⋊C8 |
| LCS | G ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,241|a^2=d,d^2=e,b^a=bc,f^b=f^2401940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C8×D241, C2×#21440554, #29507679, … |
| maximal normal subgroup of | C22⋊C8×D241, C2×#21440554, #29507679, … |
| maximal quotient of | #29507440, #29507442, #29507444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 58);