Finite Group Databasebeta

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C2×C3×C5×C37⋊C3 #16809685

order3330
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×C37⋊C3
unambiguous semidirect product(C2×C37)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C37)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C37)⋊C32
unambiguous semidirect product(C2×C3×C5×C37)⋊C3

Splittings

Fitting, socleC2×C3×C5×C37 ⋊ C3
derived, SylowC37 ⋊ C2×C32×C5
HallC2×C5×C37 ⋊ C32
HallC5×C37 ⋊ C2×C32
HallC2×C37 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C37⋊C3
commutator, cosocle, hypocenterC37C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C37C3
LCSG ▷ C37
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1110

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3×C25×C37⋊C3, C3×C5×D5×C37⋊C3, C2×C3×C52×C37⋊C3, …
maximal normal subgroup ofC2×C3×C25×C37⋊C3, C2×C3×C52×C37⋊C3, C2×C3×C5×C7×C37⋊C3, …
maximal quotient ofC2×C3×C25×C37⋊C3, C3×C5×D5×C37⋊C3, C2×C3×C52×C37⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3330, 25);