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C2×C7×C11×C37⋊C3 #30685294

order17094
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7×C11×C37⋊C3
unambiguous semidirect product(C2×C37)⋊(C3×C7×C11)
unambiguous semidirect product(C2×C11×C37)⋊(C3×C7)

Splittings

Fitting, socle, HallC2×C7×C11×C37 ⋊ C3
derived, SylowC37 ⋊ C2×C3×C7×C11
HallC7×C11×C37 ⋊ C2×C3
HallC2×C11×C37 ⋊ C3×C7
HallC2×C7×C37 ⋊ C3×C11
HallC11×C37 ⋊ C2×C3×C7
HallC7×C37 ⋊ C2×C3×C11
HallC2×C37 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11C37⋊C3
commutator, cosocle, hypocenterC37C2×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C37C3
LCSG ▷ C37
UCSC1 ◁ C2×C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5698

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C7×C11×C37⋊C3, C7×C11×Dic37⋊C3, C7×Dic11×C37⋊C3, …
maximal normal subgroup ofC4×C7×C11×C37⋊C3, C7×C11×Dic37⋊C3, C7×Dic11×C37⋊C3, …
maximal quotient ofC4×C7×C11×C37⋊C3, C22×C7×C11×C37⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17094, 2);