Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C191 · Schur multiplier (H2) = C22 |
| direct product | C22⋊Q8×C191 |
| unambiguous semidirect product | C22⋊(Q8×C191) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C191 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C191 |
| prime radical | C23×C191 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C191 ◁ G | |
74 conjugacy classes of subgroups.
2674 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #328×C191, #450×C191, #451×C191, … |
| maximal normal subgroup of | #328×C191, #450×C191, #451×C191, … |
| maximal quotient of | #380×C191, #385×C191, #387×C191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 29);