Finite Group DatabasebetaFinite Group Databasebeta| order | 26100 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#15668527⋊C3 |
| unambiguous semidirect product | #15668527⋊C32 |
| unambiguous semidirect product | (C3×#15668527)⋊C3 |
| Fitting, socle | C3×C52×C29 ⋊ C3×C4 |
| derived, Hall | C52×C29 ⋊ C32×C4 |
| Hall | C3×C29×C52⋊C3 ⋊ C4 |
| Hall | #15668527 ⋊ C32 |
| Hall | C3×C52⋊C3 ⋊ Dic29 |
| Sylow | C29 ⋊ C3×#1043⋊C3 |
| Sylow | C52 ⋊ C32×Dic29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15668527⋊C3 |
| commutator, hypocenter | C52×C29 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C29 | C3×C4 |
| prime radical | C3×C29×(C5⋊D5)⋊C3 | C2 |
| cosocle | C29×C5⋊D5 | C2×C32 |
| LCS | G ▷ C52×C29 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1305 |
462 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26100, 267);