Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C22⋊D191 |
| Fitting | C22×C4×C191 ⋊ C2 |
| Sylow | C191 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D191 |
| commutator | C2×C191 | C22×C4 |
| Frattini | C22 | C22×D191 |
| Fitting | C22×C4×C191 | C2 |
| socle | C22×C191 | C23 |
| hypercenter | C22×C4 | D191 |
| hypocenter | C191 | C4×D4 |
| LCS | G ▷ C2×C191 ▷ C191 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
94 conjugacy classes of subgroups.
1540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C22⋊D191)⋊C8, C8×C22⋊D191, #27132731, … |
| maximal normal subgroup of | (C22⋊D191)⋊C8, C8×C22⋊D191, #27132731, … |
| maximal quotient of | C4×C22⋊Dic191, C4×(C2×D191)⋊C4, C4×Dic191⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 107);