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C37×C3⋊D105 #37552148

order23310
automorphism?
homologyAbelianization (H1) = C2×C37 · Schur multiplier (H2) = C3

Aliases

direct productC37×C3⋊D105
unambiguous semidirect productC3⋊(C37×D105)
unambiguous semidirect productC5⋊(C37×C3⋊D21)
unambiguous semidirect productC7⋊(C37×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C7×C37 ⋊ C2
derived, HallC32×C5×C7 ⋊ C2×C37
HallC32×C7×C37 ⋊ D5
HallC32×C5×C37 ⋊ D7
HallC5×C7×C37 ⋊ C3⋊D3
HallC32×C37 ⋊ D35
HallC7×C37 ⋊ C3⋊D15
HallC5×C37 ⋊ C3⋊D21
HallC32×C7 ⋊ D5×C37
HallC32×C5 ⋊ D7×C37
HallC5×C7 ⋊ C3⋊D3×C37
SylowC32 ⋊ C37×D35
SylowC7 ⋊ C37×C3⋊D15
SylowC5 ⋊ C37×C3⋊D21

Subgroups

subgroupG/H
center, hypercenterC37C3⋊D105
commutator, cosocle, hypocenterC32×C5×C7C2×C37
FrattiniC1G
Fitting, socleC32×C5×C7×C37C2
LCSG ▷ C32×C5×C7
UCSC1 ◁ C37

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

5883 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 167);