Finite Group Databasebeta

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C5×C7×#4296⋊C4 #37561058

order23940
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×#4296⋊C4
unambiguous semidirect product#4296⋊(C4×C5×C7)

Splittings

derived, SylowC19 ⋊ C4×C5×C7×C9
HallC5×C7×#4296 ⋊ C4
HallC5×C7×Dic19 ⋊ C9
HallC7×#4296 ⋊ C4×C5
HallC5×#4296 ⋊ C4×C7
HallC5×C7×C19 ⋊ C4×C9
HallC7×Dic19 ⋊ C5×C9
HallC5×Dic19 ⋊ C7×C9
Hall#4296 ⋊ C4×C5×C7
HallC7×C19 ⋊ C4×C5×C9
HallC5×C19 ⋊ C4×C7×C9
HallDic19 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7AGL(1,𝔽19)
commutator, hypocenterC19C4×C5×C7×C9
FrattiniC2C5×C7×AGL(1,𝔽19)
Fitting, socleC2×C5×C7×C19C2×C9
prime radicalC2×C5×C7×C19⋊C3C2×C3
cosocleC2×C19⋊C3C2×C3×C5×C7
LCSG ▷ C19
UCSC1 ◁ C2×C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2660

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 190);