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C7×C19⋊#4380 #37561502

order23940
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C3

Aliases

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

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C4
derived, HallC32×C5×C19 ⋊ C4×C7
HallC32×C7×C19 ⋊ AGL(1,𝔽5)
HallC5×C7×C19 ⋊ #157
HallC32×C5×C7 ⋊ Dic19
HallC32×C19 ⋊ C7×AGL(1,𝔽5)
HallC7×C19 ⋊ #4380
HallC5×C19 ⋊ C7×#157
HallC32×C7 ⋊ C19⋊AGL(1,𝔽5)
HallC32×C5 ⋊ C7×Dic19
HallC5×C7 ⋊ C19⋊#157
SylowC19 ⋊ C7×#4380
SylowC32 ⋊ C7×C19⋊AGL(1,𝔽5)
SylowC5 ⋊ C7×C19⋊#157

Subgroups

subgroupG/H
center, hypercenterC7C19⋊#4380
commutator, hypocenterC32×C5×C19C4×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C19C4
prime radicalC7×C19×C3⋊D15C2
cosocleC19×C3⋊D15C2×C7
LCSG ▷ C32×C5×C19
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3990

Conjugacy classes & character table

1617 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 634);