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C2×C5×(C7⋊C9)⋊D19 #37560968

order23940
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×(C7⋊C9)⋊D19
unambiguous semidirect product(C2×C7⋊C9)⋊(C5×D19)

Splittings

derived, HallC7×C19 ⋊ C22×C5×C9
HallC5×C19×C7⋊C9 ⋊ C22
HallC2×C5×D133 ⋊ C9
HallC19×C7⋊C9 ⋊ C22×C5
HallC5×C7×C19 ⋊ C22×C9
HallC2×D133 ⋊ C5×C9
HallC5×C7⋊C9 ⋊ C2×D19
HallC5×C19 ⋊ C2×D7⋊C9
HallC7⋊C9 ⋊ C2×C5×D19
HallC5×C7 ⋊ C2×C9×D19
SylowC19 ⋊ C2×C5×D7⋊C9
SylowC7 ⋊ C2×C5×C9×D19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5ΓL(1,𝔽8)⋊D19
commutator, hypocenterC7×C19C22×C5×C9
FrattiniC3C2×C5×ΓL(1,𝔽8)⋊D19
Fitting, socleC2×C3×C5×C7×C19C2×C3
prime radicalC2×C3×C5×D133C3
cosocleC3×C7×C19C22×C3×C5
LCSG ▷ C7×C19
UCSC1 ◁ C2×C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11970

Conjugacy classes & character table

1560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 100);