Finite Group DatabasebetaFinite Group Databasebeta| order | 26292 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#27190379 |
| Fitting, socle | C2×C7×C313 ⋊ C2×C3 |
| derived, Hall | C7×C313 ⋊ C22×C3 |
| Hall | C2×D7×C313 ⋊ C3 |
| Hall | #20267160 ⋊ C22 |
| Sylow | C313 ⋊ C2×AGL(1,𝔽7) |
| Hall | C2×D7 ⋊ C313⋊C3 |
| Sylow | C7 ⋊ C22×C313⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #27190379 |
| commutator, cosocle, hypocenter | C7×C313 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C313 | C2×C3 |
| LCS | G ▷ C7×C313 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4382 |
1054 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26292, 43);