Finite Group Databasebeta

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C3×AGL(1,𝔽7)×D95 #37561283

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

Aliases

direct productC3×AGL(1,𝔽7)×D95
unambiguous semidirect productD7⋊(C32×D95)
unambiguous semidirect product(C5×AGL(1,𝔽7))⋊(C3×D19)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C22×C3
derived, HallC5×C7×C19 ⋊ C22×C32
HallC3×C5×C19×ΓL(1,𝔽8) ⋊ C22
HallD7×D95 ⋊ C32
HallC3×C19×ΓL(1,𝔽8) ⋊ C2×D5
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×D19
HallC7×C19 ⋊ C2×C32×D5
HallC5×C19 ⋊ C2×C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ C2×D95
HallC5×C7 ⋊ C2×C32×D19
SylowC19 ⋊ C3×D5×AGL(1,𝔽7)
SylowC7 ⋊ C2×C32×D95
SylowC5 ⋊ C3×D19×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC3AGL(1,𝔽7)×D95
commutator, cosocle, hypocenterC5×C7×C19C22×C32
FrattiniC1G
Fitting, socleC3×C5×C7×C19C22×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C3

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

normal subgroups only

This group has 240 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) = 1995

Conjugacy classes & character table

1029 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 415);