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C37×C3⋊#1043 #26012902

order11100
isoclinismisoclinic class of C3⋊#1043
automorphism?
homologyAbelianization (H1) = C4×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×C3⋊#1043
unambiguous semidirect productC3⋊(C37×#1043)

Splittings

Fitting, socle, HallC3×C52×C37 ⋊ C4
derived, HallC3×C52 ⋊ C4×C37
HallC52×C37 ⋊ Dic3
HallC3×C37 ⋊ #1043
SylowC52 ⋊ Dic3×C37
SylowC3 ⋊ C37×#1043

Subgroups

subgroupG/H
center, hypercenterC37C3⋊#1043
commutator, hypocenterC3×C52C4×C37
FrattiniC1G
Fitting, socleC3×C52×C37C4
prime radicalC3×C37×C5⋊D5C2
cosocleC3×C5⋊D5C2×C37
LCSG ▷ C3×C52
UCSC1 ◁ C37

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

888 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×C9⋊#1043, C37×C3⋊(#1043⋊C3), C3⋊(#1043⋊(C37⋊C3)), …
maximal normal subgroup ofC37×C3⋊(#1043⋊C3), C3⋊(#1043⋊(C37⋊C3)), C37⋊C3×C3⋊#1043, …
maximal quotient ofC37×C9⋊#1043, C3×C37×C3⋊#1043, C37×C3⋊(C3⋊#1043)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11100, 175);