Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C239 · Schur multiplier (H2) = C24 |
| direct product | #541×C239 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C239 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C239 |
| prime radical | C23×C239 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C239 ◁ G | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
5258 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3120×C239, #3123×C239, #3127×C239, … |
| maximal normal subgroup of | #3120×C239, #3123×C239, #3127×C239, … |
| maximal quotient of | #2314×C239, #2320×C239, #2323×C239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 222);