Finite Group DatabasebetaFinite Group Databasebeta| order | 26908 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D217⋊D31 |
| unambiguous semidirect product | (C31⋊D31)⋊D7 |
| Fitting, socle, derived, Hall | C7×C312 ⋊ C22 |
| Sylow | C312 ⋊ C2×D7 |
| Sylow | C7 ⋊ D312 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C312 | C22 |
| LCS | G ▷ C7×C312 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 434 |
Polycyclic presentation:
2^2,7,31^2|c^a=c^6,d^a=d^30,d^b=d^30,e^b=e^301735 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26908, 22);