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C13×Dic65⋊C3 #23778404

order10140
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×Dic65⋊C3
unambiguous semidirect productDic65⋊(C3×C13)

Splittings

derivedC5×C13 ⋊ C3×C4×C13
HallC13×Dic65 ⋊ C3
HallC5×C13×C13⋊C3 ⋊ C4
HallC5×C132 ⋊ C3×C4
HallC13×C13⋊C3 ⋊ Dic5
SylowC132 ⋊ C3×Dic5
SylowC5 ⋊ C13×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C13C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C3×C4×C13
FrattiniC2C13×C5⋊(D13⋊C3)
Fitting, socleC2×C5×C132C2×C3
prime radicalC2×C5×C13×C13⋊C3C2
cosocleC2×C5×C13C2×C3×C13
LCSG ▷ C5×C13
UCSC1 ◁ C2×C13

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13⋊C3×Dic65⋊C3, C3×C13×Dic65⋊C3, C13×C3⋊(Dic65⋊C3)
maximal normal subgroup ofC13⋊C3×Dic65⋊C3, C3×C13×Dic65⋊C3
maximal quotient ofC13×Dic65⋊C9, C3×C13×Dic65⋊C3, C13×C3⋊(Dic65⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 62);