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C5×C13×Dic13⋊C3 #23778396

order10140
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C5×C13)
unambiguous semidirect product(C5×Dic13)⋊(C3×C13)

Splittings

derivedC13 ⋊ C3×C4×C5×C13
HallC5×C13×Dic13 ⋊ C3
HallC5×C13×C13⋊C3 ⋊ C4
HallC5×C132 ⋊ C3×C4
HallC13×Dic13 ⋊ C3×C5
HallC13×C13⋊C3 ⋊ C4×C5
SylowC132 ⋊ C3×C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D13⋊C3
commutator, hypocenterC13C3×C4×C5×C13
FrattiniC2C5×C13×D13⋊C3
Fitting, socleC2×C5×C132C2×C3
prime radicalC2×C5×C13×C13⋊C3C2
cosocleC2×C13C2×C3×C5×C13
LCSG ▷ C13
UCSC1 ◁ C2×C5×C13

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C13⋊C3×Dic13⋊C3, C3×C5×C13×Dic13⋊C3, C5×C13×C3⋊(Dic13⋊C3)
maximal normal subgroup ofC5×C13⋊C3×Dic13⋊C3, C3×C5×C13×Dic13⋊C3
maximal quotient ofC5×C13×Dic13⋊C9, C3×C5×C13×Dic13⋊C3, C5×C13×C3⋊(Dic13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 54);