Finite Group DatabasebetaFinite Group Databasebeta| order | 26574 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#27210790 |
| Fitting, socle, Hall | C2×C43×C103 ⋊ C3 |
| derived, Hall | C43×C103 ⋊ C2×C3 |
| Hall | C2×C103 ⋊ C43⋊C3 |
| Sylow | C103 ⋊ C2×C43⋊C3 |
| Hall | C2×C43 ⋊ C103⋊C3 |
| Sylow | C43 ⋊ C2×C103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #27210790 |
| commutator, cosocle, hypocenter | C43×C103 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C43×C103 | C3 |
| LCS | G ▷ C43×C103 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8858 |
2958 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26574, 4);