Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C43 · Schur multiplier (H2) = C27 |
| direct product | C43×#2308 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C43 | C24 |
| commutator | C22 | C23×C4×C43 |
| Frattini, cosocle | C23 | C24×C43 |
| prime radical | C23×D4×C43 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ G | |
1160 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1892 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#8746, C43×#8747, C43×#8751, … |
| maximal normal subgroup of | C43×#8746, C43×#8747, C43×#8751, … |
| maximal quotient of | C43×#13775, C43×#13776, C43×#13784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 1040);