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C3×C7×D15×C37 #37552138

order23310
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C37 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D15×C37
unambiguous semidirect productC3⋊(C3×C7×D5×C37)
unambiguous semidirect productC5⋊(C3×D3×C7×C37)

Splittings

Fitting, socle, HallC32×C5×C7×C37 ⋊ C2
derivedC3×C5 ⋊ C2×C3×C7×C37
HallC32×C7×C37 ⋊ D5
HallC32×C5×C37 ⋊ C2×C7
HallC5×C7×C37 ⋊ C3×D3
HallC32×C37 ⋊ C7×D5
HallC32×C5×C7 ⋊ C2×C37
HallC5×C37 ⋊ C3×D3×C7
HallC32×C7 ⋊ D5×C37
HallC32×C5 ⋊ C2×C7×C37
HallC5×C7 ⋊ C3×D3×C37
SylowC32 ⋊ C7×D5×C37
SylowC5 ⋊ C3×D3×C7×C37

Subgroups

subgroupG/H
center, hypercenterC3×C7×C37D15
commutator, cosocle, hypocenterC3×C5C2×C3×C7×C37
FrattiniC1G
Fitting, socleC32×C5×C7×C37C2
LCSG ▷ C3×C5
UCSC1 ◁ C3×C7×C37

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7770

Conjugacy classes & character table

6993 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 157);