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C5×(C7⋊C9)⋊D37 #37552011

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

Aliases

direct productC5×(C7⋊C9)⋊D37
unambiguous semidirect product(C7⋊C9)⋊(C5×D37)

Splittings

derived, HallC7×C37 ⋊ C2×C5×C9
HallC5×C37×C7⋊C9 ⋊ C2
HallC5×D259 ⋊ C9
HallC37×C7⋊C9 ⋊ C2×C5
HallC5×C7×C37 ⋊ C2×C9
HallD259 ⋊ C5×C9
HallC5×C7⋊C9 ⋊ D37
HallC5×C37 ⋊ D7⋊C9
HallC7⋊C9 ⋊ C5×D37
SylowC37 ⋊ C5×D7⋊C9
HallC5×C7 ⋊ C9×D37
SylowC7 ⋊ C5×C9×D37

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊D37
commutator, hypocenterC7×C37C2×C5×C9
FrattiniC3C5×ΓL(1,𝔽8)⋊D37
Fitting, socleC3×C5×C7×C37C2×C3
prime radicalC3×C5×D259C3
cosocleC3×C7×C37C2×C3×C5
LCSG ▷ C7×C37
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

1455 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 30);