Finite Group Databasebeta

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C7×C29×#4379 #49141529

order36540
automorphism?
homologyAbelianization (H1) = C4×C7×C29 · Schur multiplier (H2) = C3

Aliases

direct productC7×C29×#4379

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C4
derived, HallC32×C5 ⋊ C4×C7×C29
HallC32×C7×C29 ⋊ Dic5
HallC32×C5×C29 ⋊ C4×C7
HallC5×C7×C29 ⋊ #157
HallC32×C5×C7 ⋊ C4×C29
HallC32×C29 ⋊ C7×Dic5
HallC5×C29 ⋊ C7×#157
HallC32×C7 ⋊ Dic5×C29
HallC5×C7 ⋊ C29×#157
SylowC32 ⋊ C7×Dic5×C29
SylowC5 ⋊ C7×C29×#157

Subgroups

subgroupG/H
center, hypercenterC7×C29#4379
commutator, hypocenterC32×C5C4×C7×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC5×C7×C3⋊D3×C29C2
cosocleC5×C3⋊D3C2×C7×C29
LCSG ▷ C32×C5
UCSC1 ◁ C7×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6090

Conjugacy classes & character table

3654 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 371);