Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C311 |
| direct product | C33×C32⋊(C37⋊C3) |
| Fitting | C35×C37 ⋊ C3 |
| Sylow | C37 ⋊ C33×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C34 | C3×C37⋊C3 |
| commutator, cosocle | C3×C37 | C35 |
| Frattini | C3 | C34×C37⋊C3 |
| Fitting | C35×C37 | C3 |
| socle | C34×C37 | C32 |
| hypercenter | C35 | C37⋊C3 |
| hypocenter | C37 | C33×H(3,𝔽3) |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C34 ◁ C35 | |
11744 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8991 |
3213 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4014);