Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C103 · Schur multiplier (H2) = C23×C4 |
| direct product | C103×#2356 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C103 | C24 |
| commutator | C22 | C23×C4×C103 |
| Frattini, cosocle | C23 | C24×C103 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C103 ◁ G | |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13184 |
5150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#8768, C103×#8769, C103×#8774, … |
| maximal normal subgroup of | C103×#8768, C103×#8769, C103×#8774, … |
| maximal quotient of | C103×#13804, C103×#13806, C103×#13810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 1088);