Finite Group Databasebeta

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C3×C11×C7⋊(C7⋊AGL(1,𝔽5)) #44568815

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C7

Aliases

direct productC3×C11×C7⋊(C7⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C4
derived, HallC5×C72 ⋊ C3×C4×C11
HallC5×C72×C11 ⋊ C3×C4
HallC3×C72×C11 ⋊ AGL(1,𝔽5)
HallC3×C5×C72 ⋊ C4×C11
HallC72×C11 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C11 ⋊ C7⋊Dic7
HallC3×C72 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ C3×C7⋊Dic7
SylowC72 ⋊ C3×C11×AGL(1,𝔽5)
HallC3×C5 ⋊ C11×C7⋊Dic7
SylowC5 ⋊ C3×C11×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC3×C11C7⋊(C7⋊AGL(1,𝔽5))
commutator, hypocenterC5×C72C3×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C72×D5×C11C2
cosocleC72×D5C2×C3×C11
LCSG ▷ C5×C72
UCSC1 ◁ C3×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

3333 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 517);