Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C191 · Schur multiplier (H2) = C2 |
| direct product | #104×C191 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C191 | D4 |
| commutator | C4 | C2×C4×C191 |
| Frattini, cosocle | C2×C4 | C22×C191 |
| socle | C2×C191 | C22⋊C4 |
| prime radical | #41×C191 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C191 ◁ C2×C4×C191 ◁ G | |
44 conjugacy classes of subgroups.
2674 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#104×C191, #421×C191, #443×C191, … |
| maximal normal subgroup of | C2×#104×C191, #421×C191, #443×C191, … |
| maximal quotient of | D4⋊C8×C191, Q8⋊C8×C191, #327×C191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 11);