Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C157 · Schur multiplier (H2) = C1 |
| direct product | #347×C157 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C157 | C42 |
| commutator | C4 | C42×C157 |
| Frattini, cosocle | C2×C8 | C22×C157 |
| socle | C2×C157 | #97 |
| prime radical | C22×C157 | M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C157 ◁ G | |
46 conjugacy classes of subgroups.
3454 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1355×C157, #1356×C157, C2×#347×C157, … |
| maximal normal subgroup of | #1355×C157, #1356×C157, C2×#347×C157, … |
| maximal quotient of | #1313×C157, #1375×C157, C2×#347×C157 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 28);