Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C157 · Schur multiplier (H2) = C2 |
| direct product | #349×C157 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C157 | C22⋊C4 |
| commutator | C22 | C2×C8×C157 |
| Frattini, cosocle | C2×C8 | C22×C157 |
| socle | C2×C157 | C22⋊C8 |
| prime radical | C23×C157 | C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C157 ◁ C2×C8×C157 ◁ G | |
58 conjugacy classes of subgroups.
3454 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1320×C157, #1321×C157, #1327×C157, … |
| maximal normal subgroup of | #1320×C157, #1321×C157, #1327×C157, … |
| maximal quotient of | #1314×C157, #1322×C157, #1330×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 30);