Finite Group DatabasebetaFinite Group Databasebeta| order | 6056 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C757 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D757 |
| commutator, hypocenter | C757 | C8 |
| Fitting | C4×C757 | C2 |
| socle | C2×C757 | C4 |
| LCS | G ▷ C757 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,757|a^2=b,b^2=c,d^a=d^7561520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D757, C2×#20258493, #27131071, … |
| maximal normal subgroup of | C8×D757, C2×#20258493, #27131071, … |
| maximal quotient of | #27131063, C2×#20258493 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6056, 6);