Finite Group DatabasebetaFinite Group Databasebeta| order | 13504 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C211 · Schur multiplier (H2) = C24 |
| direct product | #560×C211 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C211 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C211 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C211 ◁ G | |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3376 |
4009 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2200×C211, C2×#560×C211, #3529×C211, … |
| maximal normal subgroup of | #2200×C211, C2×#560×C211, #3529×C211, … |
| maximal quotient of | #2375×C211, #2376×C211, #2377×C211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13504, 241);