Finite Group DatabasebetaFinite Group Databasebeta| order | 27004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D43×D157 |
| unambiguous semidirect product | (D43×C157)⋊C2 |
| unambiguous semidirect product | (C43×D157)⋊C2 |
| unambiguous semidirect product | D6751⋊C2 |
| Fitting, socle, derived, Hall | C43×C157 ⋊ C22 |
| Sylow | C157 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×D157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C157 | C22 |
| LCS | G ▷ C43×C157 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6751 |
1840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27004, 8);