Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C157 · Schur multiplier (H2) = C23 |
| direct product | #458×C157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C157 | #120 |
| commutator, Frattini, cosocle | C23 | C23×C157 |
| prime radical | H(5,𝔽2)×C157 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C157 ◁ C23×C157 ◁ G | |
160 conjugacy classes of subgroups.
2512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2197×C157, #2198×C157, #2200×C157, … |
| maximal normal subgroup of | #2197×C157, #2198×C157, #2200×C157, … |
| maximal quotient of | #1607×C157, #1608×C157, #1609×C157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 139);