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C2×C3×C23×C37⋊C3 #29506192

order15318
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C23 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C23×C37⋊C3
unambiguous semidirect product(C2×C37)⋊(C32×C23)
unambiguous semidirect product(C2×C3×C37)⋊(C3×C23)
unambiguous semidirect product(C2×C23×C37)⋊C32
unambiguous semidirect product(C2×C3×C23×C37)⋊C3

Splittings

Fitting, socleC2×C3×C23×C37 ⋊ C3
derived, SylowC37 ⋊ C2×C32×C23
HallC2×C23×C37 ⋊ C32
HallC23×C37 ⋊ C2×C32
HallC2×C37 ⋊ C32×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23C37⋊C3
commutator, cosocle, hypocenterC37C2×C32×C23
FrattiniC1G
Fitting, socleC2×C3×C23×C37C3
LCSG ▷ C37
UCSC1 ◁ C2×C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5106

Conjugacy classes & character table

2070 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C23×Dic37⋊C3, C3×C23⋊(Dic37⋊C3), C3×Dic23×C37⋊C3, …
maximal normal subgroup ofC3×C23×Dic37⋊C3, C3×C23⋊(Dic37⋊C3), C3×Dic23×C37⋊C3, …
maximal quotient ofC3×C4×C23×C37⋊C3, C22×C3×C23×C37⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15318, 25);