Finite Group Databasebeta

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C2×C3×C5⋊#11716322 #37561459

order23940
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C5⋊#11716322
unambiguous semidirect product(C2×C5)⋊(C3×#11716322)

Splittings

Fitting, socleC2×C3×C5×C7×C19 ⋊ C2×C3
derived, HallC5×C7×C19 ⋊ C22×C32
HallC3×C5×#87705 ⋊ C22
HallC2×C7×D95 ⋊ C32
HallC3×#87705 ⋊ C2×D5
HallC2×D95 ⋊ C3×ΓL(1,𝔽8)
HallC7×C19 ⋊ C2×C32×D5
HallC5×C19 ⋊ C22×C3×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×D19⋊C3
SylowC19 ⋊ C2×C3×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C3×C5⋊(D19⋊C3)
SylowC5 ⋊ C2×C3×#11716322

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊#11716322
commutator, cosocle, hypocenterC5×C7×C19C22×C32
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C2×C3

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 3990

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 591);