Finite Group Databasebeta

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C5×C29×C7⋊#157 #49141518

order36540
automorphism?
homologyAbelianization (H1) = C4×C5×C29 · Schur multiplier (H2) = C3

Aliases

direct productC5×C29×C7⋊#157
unambiguous semidirect productC7⋊(C5×C29×#157)

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C4
derived, HallC32×C7 ⋊ C4×C5×C29
HallC32×C7×C29 ⋊ C4×C5
HallC32×C5×C29 ⋊ Dic7
HallC5×C7×C29 ⋊ #157
HallC32×C5×C7 ⋊ C4×C29
HallC32×C29 ⋊ C5×Dic7
HallC7×C29 ⋊ C5×#157
HallC32×C5 ⋊ Dic7×C29
HallC5×C7 ⋊ C29×#157
SylowC32 ⋊ C5×Dic7×C29
SylowC7 ⋊ C5×C29×#157

Subgroups

subgroupG/H
center, hypercenterC5×C29C7⋊#157
commutator, hypocenterC32×C7C4×C5×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC5×C7×C3⋊D3×C29C2
cosocleC7×C3⋊D3C2×C5×C29
LCSG ▷ C32×C7
UCSC1 ◁ C5×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6090

Conjugacy classes & character table

3480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 360);