Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #41×C193 ⋊ C2 |
| Sylow | C193 ⋊ AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×C22⋊D193 |
| commutator | C4×C193 | C23 |
| Frattini | C4 | C22×D193 |
| Fitting | #41×C193 | C2 |
| socle | C2×C193 | C2×D4 |
| hypercenter | #41 | D193 |
| hypocenter | C193 | AGL(1,ℤ/8) |
| LCS | G ▷ C4×C193 ▷ C2×C193 ▷ C193 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #41 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,193|d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^b=f^192971 conjugacy classes — view the full character table.
| maximal subgroup of | #27135427, #27135428, #27135432, … |
| maximal normal subgroup of | #27135427, #27135428, #27135432, … |
| maximal quotient of | #27135260, #27135263, #27135302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 171);