Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C103 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×#127×C103 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C103 | C23 |
| commutator, Frattini, cosocle | C22 | C25×C103 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C103 ◁ G | |
3000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6592 |
5768 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#8339, C103×#8546, C103×#10975, … |
| maximal normal subgroup of | C103×#8339, C103×#8546, C103×#10975, … |
| maximal quotient of | C22×#384×C103, C22×#390×C103, C2×C4×#127×C103 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 2172);