Finite Group DatabasebetaFinite Group Databasebeta| order | 3380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic169 |
| derived, Sylow | C169 ⋊ C4×C5 |
| Hall | C5×C169 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D169 |
| commutator, hypocenter | C169 | C4×C5 |
| Frattini | C2×C13 | C5×D13 |
| Fitting | C2×C5×C169 | C2 |
| socle, prime radical | C2×C5×C13 | D13 |
| cosocle | C2×C169 | C2×C5 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C2×C5 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 178 |
| transitive degree | μt(G) = 3380 |
860 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×Dic169, C52×Dic169, C5×Dic845, … |
| maximal normal subgroup of | C25×Dic169, C52×Dic169, C5×C7×Dic169, … |
| maximal quotient of | C25×Dic169, C52×Dic169, C5×Dic845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3380, 3);