Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C39 |
| direct product | C37⋊C3×H(5,𝔽3) |
| Fitting | C37×H(5,𝔽3) ⋊ C3 |
| Sylow | C37 ⋊ C3×H(5,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C34×C37⋊C3 |
| commutator, socle, cosocle | C3×C37 | C35 |
| Fitting | C37×H(5,𝔽3) | C3 |
| hypercenter | H(5,𝔽3) | C37⋊C3 |
| hypocenter | C37 | C3×H(5,𝔽3) |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C3 ◁ H(5,𝔽3) | |
6776 conjugacy classes of subgroups.
| transitive degree | μt(G) = 999 |
1245 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4023);