Finite Group DatabasebetaFinite Group Databasebeta| order | 27300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C3⋊#13049934 |
| unambiguous semidirect product | C3⋊(C7×#13049934) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊#13049934 |
| commutator, hypocenter | C3×C52×C13 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7×C13 | C4 |
| prime radical | C3×C5×C7×D65 | C2 |
| cosocle | C3×C5×D65 | C2×C7 |
| LCS | G ▷ C3×C52×C13 | |
| UCS | C1 ◁ C7 | |
104 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5460 |
1806 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27300, 893);