Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C41 · Schur multiplier (H2) = C29 |
| direct product | C2×C41×#568 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | C24 |
| commutator | C2 | C24×C4×C41 |
| Frattini, cosocle | C4 | C25×C41 |
| socle | C22×C41 | C23×C4 |
| prime radical | C22×#41×C41 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ G | |
1460 conjugacy classes of subgroups.
2788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#10742, C41×#10744, C41×#10746, … |
| maximal normal subgroup of | C41×#10742, C41×#10744, C41×#10746, … |
| maximal quotient of | C2×C41×#2873, C2×C41×#2875, C4×C41×#568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2304);