Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C43 · Schur multiplier (H2) = C28 |
| direct product | C43×#3532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C43 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ G | |
1336 conjugacy classes of subgroups.
1634 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#12753, C43×#33551, C2×C43×#3532, … |
| maximal normal subgroup of | C43×#12753, C43×#33551, C2×C43×#3532, … |
| maximal quotient of | C43×#34356, C43×#34406, C43×#34407, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2264);