Finite Group DatabasebetaFinite Group Databasebeta| order | 3380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C132 ⋊ C4 |
| Sylow | C132 ⋊ Dic5 |
| Sylow | C5 ⋊ #10621728 |
| 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 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 845 |
Polycyclic presentation:
2^2,5,13^2|a^2=b,c^a=c^4,d^a=d^5,e^a=e^5,d^b=d^12,e^b=e^12218 conjugacy classes — view the full character table.
| maximal subgroup of | #30683399, C5×#16810010, #30683464, … |
| maximal normal subgroup of | C5×#16810010, #16810010⋊C7, C7×#16810010, … |
| maximal quotient of | #30683399, C5×#16810010, #30683464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3380, 40);