Finite Group Databasebeta

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C2×C5×C13⋊C3×C43 #30680779

order16770
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C43 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C13⋊C3×C43
unambiguous semidirect product(C2×C13)⋊(C3×C5×C43)
unambiguous semidirect product(C2×C5×C13)⋊(C3×C43)

Splittings

Fitting, socle, HallC2×C5×C13×C43 ⋊ C3
derived, SylowC13 ⋊ C2×C3×C5×C43
HallC5×C13×C43 ⋊ C2×C3
HallC2×C13×C43 ⋊ C3×C5
HallC13×C43 ⋊ C2×C3×C5
HallC2×C5×C13 ⋊ C3×C43
HallC5×C13 ⋊ C2×C3×C43
HallC2×C13 ⋊ C3×C5×C43

Subgroups

subgroupG/H
center, hypercenterC2×C5×C43C13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C43
FrattiniC1G
Fitting, socleC2×C5×C13×C43C3
LCSG ▷ C13
UCSC1 ◁ C2×C5×C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5590

Conjugacy classes & character table

3010 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C13⋊C3×C43, C5×C13⋊C3×Dic43, C5×C43×Dic13⋊C3, …
maximal normal subgroup ofC4×C5×C13⋊C3×C43, C5×C13⋊C3×Dic43, C5×C43×Dic13⋊C3, …
maximal quotient ofC4×C5×C13⋊C3×C43, C22×C5×C13⋊C3×C43

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16770, 3);