Finite Group DatabasebetaFinite Group Databasebeta| order | 26908 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C31 |
| unambiguous semidirect product | C7⋊(C31⋊Dic31) |
| unambiguous semidirect product | C31⋊Dic217 |
| derived, Hall | C7×C312 ⋊ C4 |
| Sylow | C312 ⋊ Dic7 |
| Sylow | C7 ⋊ C31⋊Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(C31⋊D31) |
| commutator, hypocenter | C7×C312 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C7×C312 | C2 |
| LCS | G ▷ C7×C312 | |
| UCS | C1 ◁ C2 | |
204 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26908 |
Polycyclic presentation:
2,7,31^2,2|a^2=e,b^a=b^6,c^a=c^30,d^a=d^306730 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26908, 11);