Finite Group Databasebeta

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C5×C7×C3⋊(C3⋊#1181) #49141630

order36540
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC5×C7×C3⋊(C3⋊#1181)
unambiguous semidirect productC3⋊(C5×C7×C3⋊#1181)

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C4
derived, HallC32×C29 ⋊ C4×C5×C7
HallC32×C7×C29 ⋊ C4×C5
HallC32×C5×C29 ⋊ C4×C7
HallC5×C7×C29 ⋊ C3⋊Dic3
HallC32×C5×C7 ⋊ #1181
HallC7×C29 ⋊ C5×C3⋊Dic3
HallC5×C29 ⋊ C7×C3⋊Dic3
HallC32×C7 ⋊ C5×#1181
HallC32×C5 ⋊ C7×#1181
SylowC29 ⋊ C5×C7×C3⋊Dic3
SylowC32 ⋊ C5×C7×#1181

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊(C3⋊#1181)
commutator, hypocenterC32×C29C4×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC32×C5×C7×D29C2
cosocleC32×D29C2×C5×C7
LCSG ▷ C32×C29
UCSC1 ◁ C5×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

2625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 472);