Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C36 · Schur multiplier (H2) = C315 |
| direct product | C35×C37⋊C3 |
| unambiguous semidirect product | C37⋊C36 |
| unambiguous semidirect product | (C3×C37)⋊C35 |
| Fitting, socle | C35×C37 ⋊ C3 |
| derived, Sylow | C37 ⋊ C36 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C35 | C37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C36 |
| Frattini | C1 | G |
| Fitting, socle | C35×C37 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C35 | |
113264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8991 |
3645 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4033);