Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C41 · Schur multiplier (H2) = C23 |
| direct product | C41×#2055 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C22×D4×C41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C2×C42×C41 ◁ G | |
324 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C41×#2055, C41×#23539, C41×#23541, … |
| maximal normal subgroup of | C2×C41×#2055, C41×#23539, C41×#23541, … |
| maximal quotient of | C41×#10474, C41×#10475, C41×#10476, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 787);