Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C41 · Schur multiplier (H2) = C28 |
| direct product | C41×#3531 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C41 |
| socle | C22×C41 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ G | |
930 conjugacy classes of subgroups; only the 760 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 760 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1558 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8505, C41×#18990, C41×#18991, … |
| maximal normal subgroup of | C41×#8505, C41×#18990, C41×#18991, … |
| maximal quotient of | C41×#34348, C41×#34350, C4×C41×#562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2263);