Finite Group DatabasebetaFinite Group Databasebeta| order | 3380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C5×C169 ⋊ C4 |
| Sylow | C169 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #10621721 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C169 | C4 |
| Frattini | C13 | #63121 |
| socle | C5×C13 | #261 |
| prime radical, cosocle | D845 | C2 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 174 |
| transitive degree | μt(G) = 845 |
Polycyclic presentation:
2^2,5,13^2|a^2=b,d^13=e^2,c^a=c^2,d^a=d^8e,e^a=e^8,c^b=c^4,d^b=d^12e^11,e^b=e^12215 conjugacy classes — view the full character table.
| maximal subgroup of | #30683334, C5×#16809980, #30683354, … |
| maximal normal subgroup of | C5×#16809980, C7×#16809980, C11×#16809980 |
| maximal quotient of | #30683334, C5×#16809980, #30683354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3380, 10);