Finite Group DatabasebetaFinite Group Databasebeta| order | 3380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C132 ⋊ C4 |
| Sylow | C132 ⋊ Dic5 |
| Sylow | C5 ⋊ #10621729 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C132 | C4 |
| prime radical, cosocle | C5×C13⋊D13 | C2 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 130 |
Polycyclic presentation:
2^2,5,13^2|a^2=b,c^a=c^4,d^a=d^5,e^a=e^8,d^b=d^12,e^b=e^12218 conjugacy classes — view the full character table.
| maximal subgroup of | #30683400, C5×#16810011, #30683466, … |
| maximal normal subgroup of | C5×#16810011, C7×#16810011, C11×#16810011 |
| maximal quotient of | #30683400, C5×#16810011, #30683466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3380, 41);