Finite Group Databasebeta

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C32×C5×C7×#1181 #49141535

order36540
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C7×#1181

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C4
derived, SylowC29 ⋊ C32×C4×C5×C7
HallC32×C7×C29 ⋊ C4×C5
HallC32×C5×C29 ⋊ C4×C7
HallC5×C7×C29 ⋊ C32×C4
HallC32×C29 ⋊ C4×C5×C7
HallC7×C29 ⋊ C32×C4×C5
HallC5×C29 ⋊ C32×C4×C7

Subgroups

subgroupG/H
center, hypercenterC32×C5×C7#1181
commutator, hypocenterC29C32×C4×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC32×C5×C7×D29C2
cosocleD29C2×C32×C5×C7
LCSG ▷ C29
UCSC1 ◁ C32×C5×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

3465 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 377);