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C3×C5×(C37⋊C3)⋊D7 #37552073

order23310
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×(C37⋊C3)⋊D7
unambiguous semidirect product(C37⋊C3)⋊(C3×C5×D7)

Splittings

Fitting, socleC3×C5×C7×C37 ⋊ C2×C3
derived, HallC7×C37 ⋊ C2×C32×C5
HallC3×C5×C7×C37⋊C3 ⋊ C2
HallC5×D259 ⋊ C32
HallC3×C7×C37⋊C3 ⋊ C2×C5
HallC3×C5×C37⋊C3 ⋊ D7
HallC5×C7×C37 ⋊ C2×C32
HallD259 ⋊ C32×C5
HallC3×C37⋊C3 ⋊ C5×D7
HallC5×C37 ⋊ C32×D7
SylowC37 ⋊ C32×C5×D7
HallC5×C7 ⋊ C3×D37⋊C3
SylowC7 ⋊ C3×C5×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5(C37⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C37C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C37C2×C3
LCSG ▷ C7×C37
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3885

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 92);