Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C157 · Schur multiplier (H2) = C22 |
| direct product | #444×C157 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C157 | C2×D4 |
| commutator | C4 | C22×C4×C157 |
| Frattini, cosocle | C2×C4 | C23×C157 |
| socle | C2×C157 | C4×D4 |
| prime radical | #135×C157 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C157 ◁ C2×C8×C157 ◁ G | |
104 conjugacy classes of subgroups.
3454 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2180×C157, AGL(1,ℤ/16)×C157, C2×#444×C157, … |
| maximal normal subgroup of | #2180×C157, AGL(1,ℤ/16)×C157, C2×#444×C157, … |
| maximal quotient of | SD16⋊C8×C157, #1579×C157, #1580×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 125);