Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C41 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C41×#498 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C41 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G | |
424 conjugacy classes of subgroups.
1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#9059, C41×#9729, C41×#9741, … |
| maximal normal subgroup of | C41×#9059, C41×#9729, C41×#9741, … |
| maximal quotient of | C2×C41×#1844, C2×C41×#1941, C2×C41×#1990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1889);