Finite Group DatabasebetaFinite Group Databasebeta| order | 3204 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C89 ⋊ C4 |
| Sylow | C89 ⋊ #157 |
| Sylow | C32 ⋊ #67063 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C89 | C4 |
| prime radical, cosocle | C3⋊D267 | C2 |
| LCS | G ▷ C32×C89 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 534 |
Polycyclic presentation:
2^2,3^2,89|a^2=b,c^a=cd,d^a=cd^2,e^a=e^55,c^b=c^2,d^b=d^2,e^b=e^88204 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#15691978, #30630890, #30630891, … |
| maximal normal subgroup of | C5×#15691978, C7×#15691978, #15691978⋊C11, … |
| maximal quotient of | C5×#15691978, #30630890, #30630891, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3204, 29);