Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C43 · Schur multiplier (H2) = C23×C4 |
| direct product | C43×#2633 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C43 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C43 |
| prime radical | C22×D4×C43 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C43 ◁ G | |
512 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#9189, C43×#10019, C43×#10023, … |
| maximal normal subgroup of | C43×#9189, C43×#10019, C43×#10023, … |
| maximal quotient of | C43×#14269, C43×#14289, C43×#14298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 1365);