Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C41 · Schur multiplier (H2) = C22 |
| direct product | C2×C41×#330 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C41 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C41 |
| Frattini, cosocle | C42 | C23×C41 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G | |
232 conjugacy classes of subgroups.
1558 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C41×#330, C41×#8225, C41×#8227, … |
| maximal normal subgroup of | C4×C41×#330, C41×#8225, C41×#8227, … |
| maximal quotient of | C2×C41×#1271, C41×#7568, C41×#7627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 255);