Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C103 · Schur multiplier (H2) = C29 |
| direct product | C2×#534×C103 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C103 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C103 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C103 ◁ G | |
1984 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3296 |
4532 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#8403, C103×#10972, C103×#10995, … |
| maximal normal subgroup of | C103×#8403, C103×#10972, C103×#10995, … |
| maximal quotient of | C2×C103×#2308, C2×C103×#2315, C2×C103×#2321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 2177);