Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1032192 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C8 |
| abelian | C2×C82×C43 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C42 | C23×C43 |
| socle | C23×C43 | C42 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
280 conjugacy classes of subgroups.
5504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#7136, C43×#7138, C43×#7151, … |
| maximal normal subgroup of | C43×#7136, C43×#7138, C43×#7151, … |
| maximal quotient of | C4×C82×C43, C2×C43×#1273, C43×#8131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 179);