Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| isoclinism | isoclinic class of D191 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C16×D191 |
| Fitting | C16×C191 ⋊ C2 |
| derived, Sylow | C191 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | D191 |
| commutator, hypocenter | C191 | C2×C16 |
| Frattini | C8 | C2×D191 |
| Fitting | C16×C191 | C2 |
| socle | C2×C191 | C2×C8 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C16 | |
28 conjugacy classes of subgroups.
1552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D191, #27132496, C2×C16×D191, … |
| maximal normal subgroup of | C32×D191, #27132496, C2×C16×D191, … |
| maximal quotient of | C16×Dic191, (C2×D191)⋊C16, Dic191⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 83);