Finite Group DatabasebetaFinite Group Databasebeta| order | 26908 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C31 |
| direct product | C2×C7⋊(C31⋊D31) |
| unambiguous semidirect product | (C2×C7)⋊(C31⋊D31) |
| unambiguous semidirect product | (C2×C31)⋊D217 |
| Fitting, socle | C2×C7×C312 ⋊ C2 |
| derived, Hall | C7×C312 ⋊ C22 |
| Sylow | C312 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×C31⋊D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊(C31⋊D31) |
| commutator, cosocle, hypocenter | C7×C312 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C312 | C2 |
| LCS | G ▷ C7×C312 | |
| UCS | C1 ◁ C2 | |
340 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13454 |
6730 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26908, 28);