Finite Group DatabasebetaFinite Group Databasebeta| order | 18354 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | D7×C23×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D7×C19⋊C3 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C23 | C2×C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C23 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3059 |
1035 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C23×D19⋊C3, D7×C23⋊(D19⋊C3), D7×D23×C19⋊C3, … |
| maximal normal subgroup of | D7×C23×D19⋊C3, D7×C23⋊(D19⋊C3), D7×D23×C19⋊C3, … |
| maximal quotient of | C23×Dic7×C19⋊C3, C2×D7×C23×C19⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18354, 33);