Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C41 · Schur multiplier (H2) = C29 |
| direct product | C41×#3584 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C41 | C22×D4 |
| commutator, Frattini, cosocle | C4 | C25×C41 |
| socle | C2×C41 | C23×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C2×#41×C41 ◁ G | |
1424 conjugacy classes of subgroups.
1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#12745, C41×#12746, C41×#12747, … |
| maximal normal subgroup of | C41×#12745, C41×#12746, C41×#12747, … |
| maximal quotient of | C41×#60086, C41×#60108, C41×#60161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2316);