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C2×C3×D3×C11×C13 #19104250

order5148
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D3×C11×C13
unambiguous semidirect productC3⋊(C22×C3×C11×C13)
unambiguous semidirect product(C2×C3)⋊(C2×C3×C11×C13)

Splittings

Fitting, socleC2×C32×C11×C13 ⋊ C2
derivedC3 ⋊ C22×C3×C11×C13
HallC32×C11×C13 ⋊ C22
HallC32×C13 ⋊ C22×C11
HallC32×C11 ⋊ C22×C13
SylowC32 ⋊ C22×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C13D3
commutator, hypocenterC3C22×C3×C11×C13
FrattiniC1G
Fitting, socleC2×C32×C11×C13C2
LCSG ▷ C3
UCSC1 ◁ C2×C3×C11×C13

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2574 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×D3×C13×C11⋊C5, C3×D3×D5×C11×C13, C2×C3×C5×D3×C11×C13, …
maximal normal subgroup ofC2×C3×D3×C13×C11⋊C5, C2×C3×C5×D3×C11×C13, C2×C3×D3×C7×C11×C13
maximal quotient ofC3×D3×D5×C11×C13, C2×C3×C5×D3×C11×C13, C2×C3×C11×C13×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 126);