Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C41 · Schur multiplier (H2) = C22 |
| direct product | C41×#2091 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C41 | #127 |
| commutator, Frattini, cosocle | C22×C4 | C23×C41 |
| socle | C2×C41 | #399 |
| prime radical | C24×C41 | Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C22×C4×C41 ◁ G | |
222 conjugacy classes of subgroups.
1066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7432, C41×#7433, C41×#12298, … |
| maximal normal subgroup of | C41×#7432, C41×#7433, C41×#12298, … |
| maximal quotient of | C41×#10659, C41×#10660, C41×#10661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 823);