Finite Group Databasebeta

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C2×C5×C7×#4294⋊C2 #37560962

order23940
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×#4294⋊C2
unambiguous semidirect product#4294⋊(C22×C5×C7)
unambiguous semidirect product(C2×#4294)⋊(C2×C5×C7)

Splittings

derived, SylowC19 ⋊ C22×C5×C7×C9
HallC5×C7×#4294 ⋊ C22
HallC2×C5×C7×D19 ⋊ C9
HallC7×#4294 ⋊ C22×C5
HallC5×#4294 ⋊ C22×C7
HallC5×C7×C19 ⋊ C22×C9
HallC2×C7×D19 ⋊ C5×C9
HallC2×C5×D19 ⋊ C7×C9
Hall#4294 ⋊ C22×C5×C7
HallC7×C19 ⋊ C22×C5×C9
HallC5×C19 ⋊ C22×C7×C9
HallC2×D19 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7D19⋊C3
commutator, hypocenterC19C22×C5×C7×C9
FrattiniC3C2×C5×C7×D19⋊C3
Fitting, socleC2×C3×C5×C7×C19C2×C3
prime radicalC2×C3×C5×C7×D19C3
cosocleC3×C19C22×C3×C5×C7
LCSG ▷ C19
UCSC1 ◁ C2×C3×C5×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11970

Conjugacy classes & character table

1890 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 94);