Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C41 · Schur multiplier (H2) = C22 |
| direct product | C41×#2153 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C41 | C2×D4 |
| commutator | C4 | C22×C8×C41 |
| Frattini, cosocle | C2×C8 | C23×C41 |
| socle | C2×C41 | C2×C4⋊C8 |
| prime radical | C23×C41 | M16 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C41 ◁ C22×C8×C41 ◁ G | |
152 conjugacy classes of subgroups.
1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#11989, C41×#11990, C41×#11991, … |
| maximal normal subgroup of | C41×#11989, C41×#11990, C41×#11991, … |
| maximal quotient of | C41×#11997, C41×#12005, C41×#12014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 885);