Finite Group DatabasebetaFinite Group Databasebeta| order | 18916 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C4729 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4729 | C4 |
| prime radical, cosocle | D4729 | C2 |
| LCS | G ▷ C4729 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4729 |
Polycyclic presentation:
2^2,4729|a^2=b,c^a=c^3364,c^b=c^47281186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#34038692, #49180847 |
| maximal normal subgroup of | C2×#34038692, #49180847 |
| maximal quotient of | #49180845, C2×#34038692 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18916, 3);