Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×C22⋊D191 |
| Fitting | C24×C191 ⋊ C2 |
| Sylow | C191 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D191 |
| commutator | C2×C191 | C24 |
| Frattini | C2 | C23×D191 |
| Fitting | C24×C191 | C2 |
| socle | C23×C191 | C22 |
| hypercenter | C24 | D191 |
| hypocenter | C191 | C22×D4 |
| LCS | G ▷ C2×C191 ▷ C191 | |
| UCS | C1 ◁ C23 ◁ C24 | |
236 conjugacy classes of subgroups.
1540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27132539, #27132540, #27132542, … |
| maximal normal subgroup of | #27132539, #27132540, #27132542, … |
| maximal quotient of | C22×(C2×D191)⋊C4, C22×C22⋊Dic191, C22×Dic191⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 183);