Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C43 · Schur multiplier (H2) = C2×C4 |
| direct product | C43×#2248 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C43 |
| prime radical | C43×#493 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C42×C43 ◁ C4×C8×C43 ◁ G | |
196 conjugacy classes of subgroups.
1634 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#12318, C43×#12319, C43×#12320, … |
| maximal normal subgroup of | C43×#12318, C43×#12319, C43×#12320, … |
| maximal quotient of | C43×#12505, C43×#12509, C43×#12510, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 980);