Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C43 · Schur multiplier (H2) = C29 |
| direct product | C22×C4×Q8×C43 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C43 | C22 |
| commutator | C2 | C24×C4×C43 |
| Frattini, cosocle | C22 | C25×C43 |
| socle, prime radical | C24×C43 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C43 ◁ G | |
1664 conjugacy classes of subgroups.
3440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#8303, C43×#8311, C43×#10763, … |
| maximal normal subgroup of | C43×#8303, C43×#8311, C43×#10763, … |
| maximal quotient of | C22×C4×C4⋊C4×C43, C2×C42×Q8×C43, C22×C43×#387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2155);