Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1343 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C41 · Schur multiplier (H2) = C2 |
| direct product | C41×#1354 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | #99 |
| commutator | C22×C4 | C2×C4×C41 |
| Frattini, cosocle | C2×C4⋊C4 | C22×C41 |
| prime radical | C23×C41 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C41 ◁ C2×C4⋊C4×C41 ◁ G | |
140 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
943 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C41×#1354, C41×#11721, C41×#11722, … |
| maximal normal subgroup of | C2×C41×#1354, C41×#11721, C41×#11722, … |
| maximal quotient of | C41×#7123, C41×#7131, C41×#7251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 86);