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C3×C72×C11⋊AGL(1,𝔽5) #44568812

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

Aliases

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

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C4
derived, HallC5×C11 ⋊ C3×C4×C72
HallC5×C72×C11 ⋊ C3×C4
HallC3×C72×C11 ⋊ AGL(1,𝔽5)
HallC3×C5×C72 ⋊ Dic11
HallC72×C11 ⋊ C3×AGL(1,𝔽5)
HallC5×C72 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ C4×C72
HallC3×C11 ⋊ C72×AGL(1,𝔽5)
HallC3×C5 ⋊ C72×Dic11
SylowC11 ⋊ C3×C72×AGL(1,𝔽5)
SylowC5 ⋊ C3×C72×Dic11

Subgroups

subgroupG/H
center, hypercenterC3×C72C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C3×C4×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C72×D5×C11C2
cosocleD5×C11C2×C3×C72
LCSG ▷ C5×C11
UCSC1 ◁ C3×C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

3675 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 514);