Finite Group DatabasebetaFinite Group Databasebeta| order | 18693 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#20262033 |
| Fitting, socle | C3×C31×C67 ⋊ C3 |
| derived, Hall | C31×C67 ⋊ C32 |
| Sylow | C67 ⋊ C3×C31⋊C3 |
| Sylow | C31 ⋊ C3×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #20262033 |
| commutator, cosocle, hypocenter | C31×C67 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C67 | C3 |
| LCS | G ▷ C31×C67 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6231 |
2085 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#27159581, C3×#27159577, C3×#27159573, … |
| maximal normal subgroup of | C3×#27159581, C3×#27159577, C3×#27159573, … |
| maximal quotient of | C2×C3×#20262033 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18693, 8);