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C2×C5×C13⋊C3×C47 #32913293

order18330
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C47 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C13⋊C3×C47
unambiguous semidirect product(C2×C13)⋊(C3×C5×C47)
unambiguous semidirect product(C2×C5×C13)⋊(C3×C47)
unambiguous semidirect product(C2×C13×C47)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C13×C47)⋊C3

Splittings

Fitting, socle, HallC2×C5×C13×C47 ⋊ C3
derived, SylowC13 ⋊ C2×C3×C5×C47
HallC5×C13×C47 ⋊ C2×C3
HallC2×C13×C47 ⋊ C3×C5
HallC13×C47 ⋊ C2×C3×C5
HallC2×C5×C13 ⋊ C3×C47
HallC5×C13 ⋊ C2×C3×C47
HallC2×C13 ⋊ C3×C5×C47

Subgroups

subgroupG/H
center, hypercenterC2×C5×C47C13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C47
FrattiniC1G
Fitting, socleC2×C5×C13×C47C3
LCSG ▷ C13
UCSC1 ◁ C2×C5×C47

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6110

Conjugacy classes & character table

3290 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C13⋊C3×C47, C5×C13⋊C3×Dic47, C5×C47×Dic13⋊C3, …
maximal normal subgroup ofC4×C5×C13⋊C3×C47, C5×C13⋊C3×Dic47, C5×C47×Dic13⋊C3, …
maximal quotient ofC4×C5×C13⋊C3×C47, C22×C5×C13⋊C3×C47

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18330, 2);