Finite Group DatabasebetaFinite Group Databasebeta| order | 18963 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C43 · Schur multiplier (H2) = C3 |
| direct product | C3×C43×#3861 |
| Fitting, socle | C3×C72×C43 ⋊ C3 |
| derived, Sylow | C72 ⋊ C32×C43 |
| Hall | C72×C43 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C43 | #3861 |
| commutator, cosocle, hypocenter | C72 | C32×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C43 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C43 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6321 |
2451 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D43×#3861, C3×C43×#64424, C3×#27162408, … |
| maximal normal subgroup of | C3×D43×#3861, C3×C43×#64424, C3×#27162408, … |
| maximal quotient of | C2×C3×C43×#3861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18963, 54);