Finite Group Databasebeta

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C2×C3×C5×D3×C7×C19 #37561636

order23940
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D3×C7×C19
unambiguous semidirect productC3⋊(C22×C3×C5×C7×C19)
unambiguous semidirect product(C2×C3)⋊(C2×C3×C5×C7×C19)

Splittings

Fitting, socleC2×C32×C5×C7×C19 ⋊ C2
derivedC3 ⋊ C22×C3×C5×C7×C19
HallC32×C5×C7×C19 ⋊ C22
HallC32×C7×C19 ⋊ C22×C5
HallC32×C5×C19 ⋊ C22×C7
HallC32×C5×C7 ⋊ C22×C19
HallC32×C19 ⋊ C22×C5×C7
HallC32×C7 ⋊ C22×C5×C19
HallC32×C5 ⋊ C22×C7×C19
SylowC32 ⋊ C22×C5×C7×C19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7×C19D3
commutator, cosocle, hypocenterC3C22×C3×C5×C7×C19
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C19C2
LCSG ▷ C3
UCSC1 ◁ C2×C3×C5×C7×C19

176 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 112 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

11970 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 768);