Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C43 · Schur multiplier (H2) = C23 |
| direct product | C43×#1770 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C43 | C23 |
| commutator | C22 | C2×C42×C43 |
| Frattini, cosocle | C22×C4 | C23×C43 |
| socle, prime radical | C23×C43 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C43 ◁ G | |
272 conjugacy classes of subgroups.
2408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#7168, C43×#7170, C43×#8202, … |
| maximal normal subgroup of | C43×#7168, C43×#7170, C43×#8202, … |
| maximal quotient of | C43×#8260, C43×#8261, C43×#8265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 502);