Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C157 · Schur multiplier (H2) = C22 |
| direct product | #436×C157 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C157 | C23 |
| commutator | C22 | C22×C4×C157 |
| Frattini, cosocle | C2×C4 | C23×C157 |
| socle | C22×C157 | C22×C4 |
| prime radical | C2×D4×C157 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C157 ◁ G | |
122 conjugacy classes of subgroups.
4396 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1330×C157, #1581×C157, #1583×C157, … |
| maximal normal subgroup of | #1330×C157, #1581×C157, #1583×C157, … |
| maximal quotient of | #1589×C157, #1590×C157, #1591×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 117);