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C2×C5×C3⋊(D37⋊C3) #20269116

order6660
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C3⋊(D37⋊C3)
unambiguous semidirect product(C2×C3)⋊(C5×D37⋊C3)
unambiguous semidirect product(C2×C37⋊C3)⋊(C5×D3)
unambiguous semidirect product(C2×D111)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D111)⋊C3

Splittings

Fitting, socleC2×C3×C5×C37 ⋊ C2×C3
derivedC3×C37 ⋊ C22×C3×C5
HallC3×C5×C37⋊C3 ⋊ C22
HallC3×C37⋊C3 ⋊ C22×C5
HallC5×C37 ⋊ C2×C3×D3
SylowC37 ⋊ C2×C3×C5×D3

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(D37⋊C3)
commutator, hypocenterC3×C37C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C37C2×C3
LCSG ▷ C3×C37
UCSC1 ◁ C2×C5

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

270 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C25×C3⋊(D37⋊C3), C5×D5×C3⋊(D37⋊C3), C2×C52×C3⋊(D37⋊C3), …
maximal normal subgroup ofC2×C25×C3⋊(D37⋊C3), C2×C52×C3⋊(D37⋊C3)
maximal quotient ofC2×C25×C3⋊(D37⋊C3), C5×D5×C3⋊(D37⋊C3), C2×C52×C3⋊(D37⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6660, 113);