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×#518 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C24 |
| commutator | C2 | C24×C4×C41 |
| Frattini, cosocle | C22 | C25×C41 |
| prime radical | C23×D4×C41 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
1920 conjugacy classes of subgroups.
2788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8322, C41×#10740, C41×#10745, … |
| maximal normal subgroup of | C41×#8322, C41×#10740, C41×#10745, … |
| maximal quotient of | C2×C41×#2273, C2×C41×#2274, C2×C41×#2275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2157);