Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C241 · Schur multiplier (H2) = C23 |
| direct product | #396×C241 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C241 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C241 |
| prime radical | C24×C241 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C241 ◁ G | |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7712 |
5302 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#396×C241, #2392×C241, #2396×C241, … |
| maximal normal subgroup of | C2×#396×C241, #2392×C241, #2396×C241, … |
| maximal quotient of | #1439×C241, #1441×C241, #1443×C241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 77);