Finite Group DatabasebetaFinite Group Databasebeta| order | 27004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×Dic157 |
| derived, Sylow | C157 ⋊ C4×C43 |
| Hall | C43×C157 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D157 |
| commutator, hypocenter | C157 | C4×C43 |
| Frattini | C2 | C43×D157 |
| Fitting, socle, prime radical | C2×C43×C157 | C2 |
| cosocle | C2×C157 | C2×C43 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C2×C43 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27004 |
6880 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27004, 3);