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C5×C7×Dic13⋊C3 #19129679

order5460
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C5×C7)
unambiguous semidirect product(C5×Dic13)⋊(C3×C7)

Splittings

derived, SylowC13 ⋊ C3×C4×C5×C7
HallC5×C7×Dic13 ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C4
HallC5×C7×C13 ⋊ C3×C4
HallC7×Dic13 ⋊ C3×C5
HallC7×C13⋊C3 ⋊ C4×C5
HallC5×Dic13 ⋊ C3×C7
HallC5×C13⋊C3 ⋊ C4×C7
HallC7×C13 ⋊ C3×C4×C5
HallC5×C13 ⋊ C3×C4×C7
HallDic13 ⋊ C3×C5×C7
HallC13⋊C3 ⋊ C4×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D13⋊C3
commutator, hypocenterC13C3×C4×C5×C7
FrattiniC2C5×C7×D13⋊C3
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

560 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×ΓL(1,𝔽8)×Dic13⋊C3, C3×C5×C7×Dic13⋊C3, C5×C7×C3⋊(Dic13⋊C3), …
maximal normal subgroup ofC5×ΓL(1,𝔽8)×Dic13⋊C3, C3×C5×C7×Dic13⋊C3, C7×C25×Dic13⋊C3, …
maximal quotient ofC5×C7×Dic13⋊C9, C3×C5×C7×Dic13⋊C3, C5×C7×C3⋊(Dic13⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 21);