Finite Group Databasebeta

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C2×C3×C19×D105 #37561642

order23940
automorphism?
homologyAbelianization (H1) = C22×C3×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C19×D105
unambiguous semidirect product(C2×C3)⋊(C3×C19×D35)
unambiguous semidirect product(C2×C5)⋊(C3×C19×D21)

Splittings

Fitting, socleC2×C32×C5×C7×C19 ⋊ C2
derivedC3×C5×C7 ⋊ C22×C3×C19
HallC32×C5×C7×C19 ⋊ C22
HallC32×C7×C19 ⋊ C2×D5
HallC32×C5×C19 ⋊ C2×D7
HallC5×C7×C19 ⋊ C2×C3×D3
HallC32×C5×C7 ⋊ C22×C19
HallC32×C19 ⋊ C2×D35
HallC7×C19 ⋊ C2×C3×D15
HallC5×C19 ⋊ C2×C3×D21
HallC32×C7 ⋊ C2×D5×C19
HallC32×C5 ⋊ C2×D7×C19
HallC5×C7 ⋊ C2×C3×D3×C19
SylowC32 ⋊ C2×C19×D35
SylowC7 ⋊ C2×C3×C19×D15
SylowC5 ⋊ C2×C3×C19×D21

Subgroups

subgroupG/H
center, hypercenterC2×C3×C19D105
commutator, cosocle, hypocenterC3×C5×C7C22×C3×C19
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C19C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C3×C19

176 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7980

Conjugacy classes & character table

6156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 774);