Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C41 · Schur multiplier (H2) = C2×C4 |
| direct product | C41×#1384 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C41 | #106 |
| commutator | C8 | C42×C41 |
| Frattini, cosocle | C22×C8 | C22×C41 |
| socle | C2×C41 | #340 |
| prime radical | C23×C41 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C22×C4×C41 ◁ C22×C8×C41 ◁ G | |
132 conjugacy classes of subgroups.
1312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7422, C41×#7423, C2×C41×#1384, … |
| maximal normal subgroup of | C41×#7422, C41×#7423, C2×C41×#1384, … |
| maximal quotient of | C41×#7157, C41×#7174, C41×#7218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 116);