Finite Group DatabasebetaFinite Group Databasebeta| order | 18270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D15×C29⋊C7 |
| unambiguous semidirect product | C3⋊(D15×C29⋊C7) |
| unambiguous semidirect product | C5⋊(C3⋊D3×C29⋊C7) |
| unambiguous semidirect product | (C29×C3⋊D15)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C29 | C2×C7 |
| LCS | G ▷ C32×C5×C29 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1305 |
264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #19104887⋊C7, #4380×C29⋊C7, (C3⋊(D29⋊C7))⋊D15, … |
| maximal normal subgroup of | #19104887⋊C7, #4380×C29⋊C7, (C3⋊(D29⋊C7))⋊D15, … |
| maximal quotient of | C3⋊Dic15×C29⋊C7, C2×C3⋊D15×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18270, 44);