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C5×C37×D7⋊C9 #37552007

order23310
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C37 · Schur multiplier (H2) = C1

Aliases

direct productC5×C37×D7⋊C9
unambiguous semidirect productD7⋊(C5×C9×C37)
unambiguous semidirect product(C7⋊C9)⋊(C2×C5×C37)
unambiguous semidirect product(C5×D7)⋊(C9×C37)

Splittings

derived, SylowC7 ⋊ C2×C5×C9×C37
HallC5×C37×C7⋊C9 ⋊ C2
HallC5×D7×C37 ⋊ C9
HallC37×C7⋊C9 ⋊ C2×C5
HallC5×C7×C37 ⋊ C2×C9
HallD7×C37 ⋊ C5×C9
HallC5×C7⋊C9 ⋊ C2×C37
HallC7×C37 ⋊ C2×C5×C9
HallC5×D7 ⋊ C9×C37
HallC7⋊C9 ⋊ C2×C5×C37
HallC5×C7 ⋊ C2×C9×C37
HallD7 ⋊ C5×C9×C37

Subgroups

subgroupG/H
center, hypercenterC3×C5×C37AGL(1,𝔽7)
commutator, hypocenterC7C2×C5×C9×C37
FrattiniC3C5×C37×AGL(1,𝔽7)
Fitting, socleC3×C5×C7×C37C2×C3
prime radicalC3×C5×D7×C37C3
cosocleC3×C7C2×C3×C5×C37
LCSG ▷ C7
UCSC1 ◁ C3×C5×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

3885 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 26);