Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C41 · Schur multiplier (H2) = C214 |
| direct product | C22×2−1+4×C41 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C24 |
| commutator, Frattini, cosocle | C2 | C26×C41 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
5872 conjugacy classes of subgroups.
2788 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#20587, C41×#20593, C41×#20603, … |
| maximal normal subgroup of | C41×#20587, C41×#20593, C41×#20603, … |
| maximal quotient of | C22×C41×#519, C22×C41×#520, C2×C4×2−1+4×C41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2324);