Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#13095393 |
| derived, Sylow | C193 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D193 |
| commutator, hypocenter | C193 | C4×C8 |
| Frattini | C2×C4 | C2×D193 |
| Fitting | C42×C193 | C2 |
| socle | C22×C193 | C2×C4 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C42 | |
44 conjugacy classes of subgroups.
1568 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#13095393, #27134980, #27134981, … |
| maximal normal subgroup of | C8×#13095393, #27134980, #27134981, … |
| maximal quotient of | C8×#13095393, #27134980, #27135014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 55);