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C3×C11×Dic13⋊C3 #19104166

order5148
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×Dic13⋊C3
unambiguous semidirect productDic13⋊(C32×C11)
unambiguous semidirect product(C3×Dic13)⋊(C3×C11)
unambiguous semidirect product(C11×Dic13)⋊C32
unambiguous semidirect product(C3×C11×Dic13)⋊C3

Splittings

derived, SylowC13 ⋊ C32×C4×C11
HallC3×C11×C13⋊C3 ⋊ C4
HallC11×Dic13 ⋊ C32
HallC11×C13 ⋊ C32×C4
HallC3×C13⋊C3 ⋊ C4×C11
HallDic13 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D13⋊C3
commutator, hypocenterC13C32×C4×C11
FrattiniC2C3×C11×D13⋊C3
Fitting, socleC2×C3×C11×C13C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

528 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊C5×Dic13⋊C3, C3×C5×C11×Dic13⋊C3, C3×C11×Dic65⋊C3, …
maximal normal subgroup ofC3×C11⋊C5×Dic13⋊C3, C3×C5×C11×Dic13⋊C3, C3×C7×C11×Dic13⋊C3
maximal quotient ofC3×C5×C11×Dic13⋊C3, C3×C11×Dic65⋊C3, C3×C11×#63120⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 42);