Finite Group DatabasebetaFinite Group Databasebeta| order | 14656 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C229 · Schur multiplier (H2) = C25 |
| direct product | #392×C229 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C229 | C23 |
| commutator, Frattini, cosocle | C23 | C23×C229 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C229 ◁ G | |
322 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7328 |
5038 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1343×C229, #1595×C229, #1596×C229, … |
| maximal normal subgroup of | #1343×C229, #1595×C229, #1596×C229, … |
| maximal quotient of | #1438×C229, #1439×C229, #1444×C229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14656, 73);