Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C191 · Schur multiplier (H2) = C22 |
| direct product | C4×Q8×C191 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C191 | C22 |
| commutator | C2 | C22×C4×C191 |
| Frattini, cosocle | C22 | C23×C191 |
| socle, prime radical | C22×C191 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C191 ◁ G | |
70 conjugacy classes of subgroups.
3820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×C191, C4×SD16×C191, C4×Q16×C191, … |
| maximal normal subgroup of | Q8⋊C8×C191, C4×SD16×C191, C4×Q16×C191, … |
| maximal quotient of | C4×C4⋊C4×C191, #387×C191, #389×C191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 26);