Finite Group Databasebeta

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C72×C3⋊(C11⋊AGL(1,𝔽5)) #44568860

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

Aliases

direct productC72×C3⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C72×C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C72×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C4
derived, HallC3×C5×C11 ⋊ C4×C72
HallC5×C72×C11 ⋊ Dic3
HallC3×C72×C11 ⋊ AGL(1,𝔽5)
HallC3×C5×C72 ⋊ Dic11
HallC72×C11 ⋊ ΓL(1,𝔽16)
HallC5×C72 ⋊ Dic33
HallC3×C72 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ C72×Dic3
HallC3×C11 ⋊ C72×AGL(1,𝔽5)
HallC3×C5 ⋊ C72×Dic11
SylowC11 ⋊ C72×ΓL(1,𝔽16)
SylowC5 ⋊ C72×Dic33
SylowC3 ⋊ C72×C11⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC72C3⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C11C4×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C72×D5×C11C2
cosocleC3×D5×C11C2×C72
LCSG ▷ C3×C5×C11
UCSC1 ◁ C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

3381 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 562);