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C13×Dic105 #19129677

order5460
isoclinismisoclinic class of D105
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×Dic105
unambiguous semidirect productC3⋊(C13×Dic35)
unambiguous semidirect productC7⋊(C13×Dic15)

Splittings

derived, HallC3×C5×C7 ⋊ C4×C13
HallC3×C5×C7×C13 ⋊ C4
HallC5×C7×C13 ⋊ Dic3
HallC3×C7×C13 ⋊ Dic5
HallC3×C5×C13 ⋊ Dic7
HallC7×C13 ⋊ Dic15
HallC5×C13 ⋊ Dic21
HallC3×C13 ⋊ Dic35
HallC5×C7 ⋊ Dic3×C13
HallC3×C7 ⋊ C13×Dic5
HallC3×C5 ⋊ C13×Dic7
SylowC7 ⋊ C13×Dic15
SylowC5 ⋊ C13×Dic21
SylowC3 ⋊ C13×Dic35

Subgroups

subgroupG/H
center, hypercenterC2×C13D105
commutator, hypocenterC3×C5×C7C4×C13
FrattiniC2C13×D105
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1404 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×Dic315, C13×C3⋊(ΓL(1,𝔽8)⋊Dic5), C3⋊#19129701, …
maximal normal subgroup ofC13×C3⋊(ΓL(1,𝔽8)⋊Dic5), C3⋊#19129701, C3⋊#19129702, …
maximal quotient ofC13×Dic315, C3×C13×Dic105, C13×C3⋊Dic105, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 19);