Finite Group DatabasebetaFinite Group Databasebeta| order | 18693 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C31×C67 ⋊ C32 |
| Sylow | C67 ⋊ C3×C31⋊C3 |
| Sylow | C31 ⋊ C3×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C67 | C32 |
| LCS | G ▷ C31×C67 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2077 |
325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C31⋊C3)⋊(D67⋊C3), D31⋊C3×C67⋊C3, C31⋊C3×D67⋊C3, … |
| maximal normal subgroup of | (C31⋊C3)⋊(D67⋊C3), D31⋊C3×C67⋊C3, C31⋊C3×D67⋊C3, … |
| maximal quotient of | C2×C31⋊C3×C67⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18693, 7);