Finite Group Databasebeta

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C2×C5⋊#14558787 #37560978

order23940
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊#14558787
unambiguous semidirect product(C2×C5)⋊#14558787

Splittings

derived, HallC5×C7×C19 ⋊ C22×C9
HallC5×#11924777 ⋊ C22
HallC2×D665 ⋊ C9
Hall#11924777 ⋊ C2×D5
HallC7×C19 ⋊ C2×C9×D5
HallC5×C19 ⋊ C2×D7⋊C9
HallC5×C7 ⋊ C2×#4294⋊C2
SylowC19 ⋊ C2×C5⋊(D7⋊C9)
SylowC7 ⋊ C2×C5⋊(#4294⋊C2)
SylowC5 ⋊ C2×#14558787

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊#11716328
commutator, hypocenterC5×C7×C19C22×C9
FrattiniC3C2×C5⋊#11716328
Fitting, socleC2×C3×C5×C7×C19C2×C3
prime radicalC2×C3×D665C3
cosocleC3×C5×C7×C19C22×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11970

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 110);