Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#13095402 |
| Fitting | C4×C193 ⋊ C8 |
| Sylow | C193 ⋊ C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#13095402 |
| commutator, socle | C2×C193 | C2×C8 |
| Fitting | C4×C193 | C8 |
| hypercenter | C4 | #13095402 |
| hypocenter | C193 | C4⋊C8 |
| LCS | G ▷ C2×C193 ▷ C193 | |
| UCS | C1 ◁ C2 ◁ C4 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,193|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^43,f^d=f^112,f^e=f^192116 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#13095402, Q8⋊#13095402, #27136348, … |
| maximal normal subgroup of | D4⋊#13095402, Q8⋊#13095402, #27136348, … |
| maximal quotient of | #27136348, #27136349, (C2×#13095402)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 239);