Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic191 |
| Sylow | C191 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D191 |
| commutator | C2×C191 | C22×C4 |
| Fitting | C2×D4×C191 | C2 |
| socle | C22×C191 | C23 |
| hypercenter | C2×D4 | D191 |
| hypocenter | C191 | C4×D4 |
| LCS | G ▷ C2×C191 ▷ C191 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
970 conjugacy classes — view the full character table.
| maximal subgroup of | #27132743, D8×Dic191, SD16×Dic191, … |
| maximal normal subgroup of | #27132743, D8×Dic191, SD16×Dic191, … |
| maximal quotient of | C22⋊C4×Dic191, C4⋊C4×Dic191, #27132538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 109);