Finite Group Databasebeta

← Prev (#30680809) Next (#30680811) →

D5×C13⋊C3×C43 #30680810

order16770
automorphism?
homologyAbelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1

Aliases

direct productD5×C13⋊C3×C43
unambiguous semidirect productC5⋊(C2×C13⋊C3×C43)
unambiguous semidirect product(D5×C13)⋊(C3×C43)

Splittings

Fitting, socle, HallC5×C13×C43 ⋊ C2×C3
derived, HallC5×C13 ⋊ C2×C3×C43
HallC5×C13⋊C3×C43 ⋊ C2
HallD5×C13×C43 ⋊ C3
HallC13×C43 ⋊ C3×D5
HallC5×C43 ⋊ C2×C13⋊C3
HallC5×C13⋊C3 ⋊ C2×C43
HallD5×C13 ⋊ C3×C43
SylowC13 ⋊ C3×D5×C43
SylowC5 ⋊ C2×C13⋊C3×C43

Subgroups

subgroupG/H
center, hypercenterC43D5×C13⋊C3
commutator, cosocle, hypocenterC5×C13C2×C3×C43
FrattiniC1G
Fitting, socleC5×C13×C43C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2795

Conjugacy classes & character table

1204 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC43×#63120⋊C3, #46776461, AGL(1,𝔽5)×C13⋊C3×C43, …
maximal normal subgroup ofC43×#63120⋊C3, #46776461, AGL(1,𝔽5)×C13⋊C3×C43, …
maximal quotient ofDic5×C13⋊C3×C43, C2×D5×C13⋊C3×C43

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16770, 34);