Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C41 · Schur multiplier (H2) = C29 |
| direct product | C2×D4×Q8×C41 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C41 |
| prime radical | C22×D4×C41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
1568 conjugacy classes of subgroups.
2050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#8379, C41×#8388, C41×#8391, … |
| maximal normal subgroup of | C41×#8379, C41×#8388, C41×#8391, … |
| maximal quotient of | C2×Q8×C22⋊C4×C41, C2×D4×C4⋊C4×C41, C2×Q8×C4⋊C4×C41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 2198);