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C11×C13×C3⋊Dic3 #19104181

order5148
isoclinismisoclinic class of C3⋊D3
automorphism?
homologyAbelianization (H1) = C4×C11×C13 · Schur multiplier (H2) = C3

Aliases

direct productC11×C13×C3⋊Dic3
unambiguous semidirect productC3⋊(C11×Dic3×C13)

Splittings

derived, SylowC32 ⋊ C4×C11×C13
HallC32×C11×C13 ⋊ C4
HallC32×C13 ⋊ C4×C11
HallC32×C11 ⋊ C4×C13

Subgroups

subgroupG/H
center, hypercenterC2×C11×C13C3⋊D3
commutator, hypocenterC32C4×C11×C13
FrattiniC2C11×C13×C3⋊D3
Fitting, socleC2×C32×C11×C13C2
LCSG ▷ C32
UCSC1 ◁ C2×C11×C13

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×C3⋊Dic3×C11⋊C5, C11×C13×C3⋊Dic15, C5×C11×C13×C3⋊Dic3, …
maximal normal subgroup ofC13×C3⋊Dic3×C11⋊C5, C5×C11×C13×C3⋊Dic3, C7×C11×C13×C3⋊Dic3
maximal quotient ofC11×C13×C3⋊Dic15, C5×C11×C13×C3⋊Dic3, C11×C13×C3⋊ΓL(1,𝔽16), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 57);