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C19×C7⋊#4380 #37561503

order23940
automorphism?
homologyAbelianization (H1) = C4×C19 · Schur multiplier (H2) = C3

Aliases

direct productC19×C7⋊#4380
unambiguous semidirect productC7⋊(C19×#4380)

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C4
derived, HallC32×C5×C7 ⋊ C4×C19
HallC32×C7×C19 ⋊ AGL(1,𝔽5)
HallC32×C5×C19 ⋊ Dic7
HallC5×C7×C19 ⋊ #157
HallC32×C19 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C19 ⋊ #4380
HallC5×C19 ⋊ C7⋊#157
HallC32×C7 ⋊ C19×AGL(1,𝔽5)
HallC32×C5 ⋊ C19×Dic7
HallC5×C7 ⋊ C19×#157
SylowC32 ⋊ C19×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C19×#4380
SylowC5 ⋊ C19×C7⋊#157

Subgroups

subgroupG/H
center, hypercenterC19C7⋊#4380
commutator, hypocenterC32×C5×C7C4×C19
FrattiniC1G
Fitting, socleC32×C5×C7×C19C4
prime radicalC7×C19×C3⋊D15C2
cosocleC7×C3⋊D15C2×C19
LCSG ▷ C32×C5×C7
UCSC1 ◁ C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3990

Conjugacy classes & character table

1653 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 635);