Finite Group DatabasebetaFinite Group Databasebeta| order | 26100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| direct product | C52⋊C3×C3⋊#1181 |
| unambiguous semidirect product | C3⋊(C52⋊C3×#1181) |
| unambiguous semidirect product | (C52×C3⋊#1181)⋊C3 |
| Fitting, socle, derived | C3×C52×C29 ⋊ C3×C4 |
| Hall | C3×C29×C52⋊C3 ⋊ C4 |
| Hall | C52×C29 ⋊ C3×Dic3 |
| Hall | C3×C52⋊C3 ⋊ #1181 |
| Sylow | C29 ⋊ Dic3×C52⋊C3 |
| Sylow | C52 ⋊ C3×C3⋊#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C29 | C3×C4 |
| prime radical | C3×D29×C52⋊C3 | C2 |
| cosocle | C3×C52×D29 | C2×C3 |
| LCS | G ▷ C3×C52×C29 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1305 |
297 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26100, 271);