Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C193 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C193 | C32 |
| LCS | G ▷ C193 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,193|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^185,f^b=f^64,f^c=f^43,f^d=f^112,f^e=f^19238 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20260000, #27136394, #72222895 |
| maximal normal subgroup of | C2×#20260000, #27136394, #72222895 |
| maximal quotient of | #27136392, C2×#20260000 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 247);