Finite Group Databasebeta

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C3×C72×Dic11⋊C5 #44568460

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC3×C72×Dic11⋊C5
unambiguous semidirect productDic11⋊(C3×C5×C72)
unambiguous semidirect product(C11⋊C5)⋊(C3×C4×C72)
unambiguous semidirect product(C3×Dic11)⋊(C5×C72)
unambiguous semidirect product(C3×C7×Dic11)⋊(C5×C7)
unambiguous semidirect product(C3×C72×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C3×C4×C5×C72
HallC3×C72×C11⋊C5 ⋊ C4
HallC3×C72×Dic11 ⋊ C5
HallC72×C11⋊C5 ⋊ C3×C4
HallC72×Dic11 ⋊ C3×C5
HallC3×C72×C11 ⋊ C4×C5
HallC72×C11 ⋊ C3×C4×C5
HallC3×C11⋊C5 ⋊ C4×C72
HallC3×Dic11 ⋊ C5×C72
HallC11⋊C5 ⋊ C3×C4×C72
HallDic11 ⋊ C3×C5×C72
HallC3×C11 ⋊ C4×C5×C72

Subgroups

subgroupG/H
center, hypercenterC2×C3×C72AGL(1,𝔽11)
commutator, hypocenterC11C3×C4×C5×C72
FrattiniC2C3×C72×AGL(1,𝔽11)
Fitting, socleC2×C3×C72×C11C2×C5
prime radicalC2×C3×C72×C11⋊C5C2
cosocleC2×C11C2×C3×C5×C72
LCSG ▷ C11
UCSC1 ◁ C2×C3×C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6468

Conjugacy classes & character table

3234 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 162);