Finite Group DatabasebetaFinite Group Databasebeta| order | 18270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5×C29 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×D7×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5×C29 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C32×C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C29 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C32×C5×C29 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9135 |
6525 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C5×D7×D29, C32×D5×D7×C29, C32×D7×D145, … |
| maximal normal subgroup of | C32×C5×D7×D29, C32×D5×D7×C29, C32×D7×D145, … |
| maximal quotient of | C32×C5×Dic7×C29, C2×C32×C5×D7×C29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18270, 83);