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C7×D15×C37⋊C3 #37552108

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

Aliases

direct productC7×D15×C37⋊C3
unambiguous semidirect productC3⋊(C7×D5×C37⋊C3)
unambiguous semidirect productC5⋊(D3×C7×C37⋊C3)
unambiguous semidirect product(D15×C37)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C37 ⋊ C2×C3
derivedC3×C5×C37 ⋊ C2×C3×C7
HallC3×C5×C7×C37⋊C3 ⋊ C2
HallC3×C7×C37⋊C3 ⋊ D5
HallC3×C5×C37⋊C3 ⋊ C2×C7
HallC5×C7×C37 ⋊ C3×D3
HallC3×C37⋊C3 ⋊ C7×D5
HallC7×C37 ⋊ C3×D15
HallC5×C37 ⋊ C3×D3×C7
SylowC37 ⋊ C3×C7×D15
HallC5×C7 ⋊ D3×C37⋊C3
SylowC5 ⋊ D3×C7×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D15×C37⋊C3
commutator, cosocle, hypocenterC3×C5×C37C2×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C37C2×C3
LCSG ▷ C3×C5×C37
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3885

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 127);