Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C193 · Schur multiplier (H2) = C2 |
| direct product | #97×C193 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C193 | C22 |
| commutator | C2 | C42×C193 |
| Frattini, cosocle | C2×C4 | C22×C193 |
| socle, prime radical | C22×C193 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C193 ◁ G | |
40 conjugacy classes of subgroups.
3860 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #329×C193, #330×C193, #347×C193, … |
| maximal normal subgroup of | #329×C193, #330×C193, #347×C193, … |
| maximal quotient of | #322×C193, #336×C193, #347×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 4);