Finite Group DatabasebetaFinite Group Databasebeta| order | 18723 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C79 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C792 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C792 | C3 |
| LCS | G ▷ C792 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 237 |
Polycyclic presentation:
3,79^2|b^a=b^23,c^a=c^552083 conjugacy classes. The character table is too large to display.
| derived subgroup of | #49153700 |
| maximal subgroup of | #49153700, #49153705, #49153707, … |
| maximal normal subgroup of | #49153700, #49153705, #49153707, … |
| maximal quotient of | C2×#34035374 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18723, 5);