Finite Group Databasebeta

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C3×C72×C11×AGL(1,𝔽5) #44568811

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C72×C11 · Schur multiplier (H2) = C7

Aliases

direct productC3×C72×C11×AGL(1,𝔽5)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C72×C11
HallC5×C72×C11 ⋊ C3×C4
HallC3×C5×C72 ⋊ C4×C11
HallC5×C72 ⋊ C3×C4×C11
HallC3×C5×C11 ⋊ C4×C72
HallC5×C11 ⋊ C3×C4×C72
HallC3×C5 ⋊ C4×C72×C11

Subgroups

subgroupG/H
center, hypercenterC3×C72×C11AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C72×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C72×D5×C11C2
cosocleD5C2×C3×C72×C11
LCSG ▷ C5
UCSC1 ◁ C3×C72×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

8085 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 513);