Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C41 · Schur multiplier (H2) = C24×C4 |
| direct product | C41×#2501 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C41 |
| prime radical | C2×#121×C41 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
708 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1558 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#9464, C41×#9952, C41×#9960, … |
| maximal normal subgroup of | C41×#9464, C41×#9952, C41×#9960, … |
| maximal quotient of | C41×#13880, C41×#13904, C41×#13996, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 1233);