Finite Group DatabasebetaFinite Group Databasebeta| order | 27904 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C109 · Schur multiplier (H2) = C27 |
| direct product | C109×#14018 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C109 | C24 |
| commutator | C23 | C23×C4×C109 |
| Frattini, cosocle | C24 | C24×C109 |
| prime radical | C23×D4×C109 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C109 ◁ G | |
2474 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13952 |
8284 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27904, 7006);