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C37×D195 #28385802

order14430
isoclinismisoclinic class of D195
automorphism?
homologyAbelianization (H1) = C2×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×D195
unambiguous semidirect productC3⋊(C37×D65)
unambiguous semidirect productC5⋊(C37×D39)
unambiguous semidirect productC13⋊(D15×C37)

Splittings

Fitting, socle, HallC3×C5×C13×C37 ⋊ C2
derived, HallC3×C5×C13 ⋊ C2×C37
HallC5×C13×C37 ⋊ D3
HallC3×C13×C37 ⋊ D5
HallC3×C5×C37 ⋊ D13
HallC13×C37 ⋊ D15
HallC5×C37 ⋊ D39
HallC3×C37 ⋊ D65
HallC5×C13 ⋊ D3×C37
HallC3×C13 ⋊ D5×C37
HallC3×C5 ⋊ D13×C37
SylowC13 ⋊ D15×C37
SylowC5 ⋊ C37×D39
SylowC3 ⋊ C37×D65

Subgroups

subgroupG/H
center, hypercenterC37D195
commutator, cosocle, hypocenterC3×C5×C13C2×C37
FrattiniC1G
Fitting, socleC3×C5×C13×C37C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7215

Conjugacy classes & character table

3663 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD37×D195, D13×D15×C37, D481⋊D15, …
maximal normal subgroup ofD37×D195, D13×D15×C37, D481⋊D15, …
maximal quotient ofC37×Dic195, C2×C37×D195

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14430, 19);