Finite Group Databasebeta

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C32×C5×C7⋊#1181 #49141536

order36540
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C7⋊#1181

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C4
derived, HallC7×C29 ⋊ C32×C4×C5
HallC32×C7×C29 ⋊ C4×C5
HallC32×C5×C29 ⋊ Dic7
HallC5×C7×C29 ⋊ C32×C4
HallC32×C5×C7 ⋊ #1181
HallC32×C29 ⋊ C5×Dic7
HallC5×C29 ⋊ C32×Dic7
HallC32×C7 ⋊ C5×#1181
HallC5×C7 ⋊ C32×#1181
SylowC29 ⋊ C32×C5×Dic7
SylowC7 ⋊ C32×C5×#1181

Subgroups

subgroupG/H
center, hypercenterC32×C5C7⋊#1181
commutator, hypocenterC7×C29C32×C4×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC32×C5×C7×D29C2
cosocleC7×D29C2×C32×C5
LCSG ▷ C7×C29
UCSC1 ◁ C32×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

2655 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 378);