Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C41 · Schur multiplier (H2) = C29 |
| direct product | C22×AGL(1,ℤ/8)×C41 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C25×C41 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C23×C4×C41 ◁ G | |
1720 conjugacy classes of subgroups.
1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#11012, C41×#11014, C41×#11016, … |
| maximal normal subgroup of | C41×#11012, C41×#11014, C41×#11016, … |
| maximal quotient of | C22×C41×#418, C22×C41×#417, C22×C41×#428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2310);