Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C43 · Schur multiplier (H2) = C29 |
| direct product | C43×#3584 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C43 | C22×D4 |
| commutator, Frattini, cosocle | C4 | C25×C43 |
| socle | C2×C43 | C23×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C43 ◁ C2×#41×C43 ◁ G | |
1424 conjugacy classes of subgroups.
1892 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#12745, C43×#12746, C43×#12747, … |
| maximal normal subgroup of | C43×#12745, C43×#12746, C43×#12747, … |
| maximal quotient of | C43×#60086, C43×#60108, C43×#60161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2316);