Finite Group DatabasebetaFinite Group Databasebeta| order | 26964 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊D749 |
| Fitting, socle, derived, Hall | C32×C7×C107 ⋊ C22 |
| Hall | C32×C107 ⋊ C2×D7 |
| Hall | C7×C107 ⋊ D32 |
| Sylow | C107 ⋊ (C3⋊D3)⋊D7 |
| Hall | C32×C7 ⋊ C2×D107 |
| Sylow | C32 ⋊ C2×D749 |
| Sylow | C7 ⋊ (C3⋊D3)⋊D107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C107 | C22 |
| LCS | G ▷ C32×C7×C107 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4494 |
Polycyclic presentation:
2^2,3^2,7,107|d^a=d^2,e^a=e^6,f^a=f^106,c^b=c^2,d^b=d^22253 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26964, 91);