Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3612672 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C16×C43 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C8 | C24×C43 |
| socle | C24×C43 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
440 conjugacy classes of subgroups.
5504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C43×#1374, C43×#12545, C2×C43×#1379, … |
| maximal normal subgroup of | C2×C43×#1374, C43×#12545, C2×C43×#1379, … |
| maximal quotient of | C22×C4×C16×C43, C22×C43×C22⋊C16, C22×C43×C4⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2136);