Finite Group Databasebeta

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C5×C7×C13×#157 #30655750

order16380
isoclinismisoclinic class of #157
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C13 · Schur multiplier (H2) = C3

Aliases

direct productC5×C7×C13×#157

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C4
derived, SylowC32 ⋊ C4×C5×C7×C13
HallC32×C7×C13 ⋊ C4×C5
HallC32×C5×C13 ⋊ C4×C7
HallC32×C5×C7 ⋊ C4×C13
HallC32×C13 ⋊ C4×C5×C7
HallC32×C7 ⋊ C4×C5×C13
HallC32×C5 ⋊ C4×C7×C13

Subgroups

subgroupG/H
center, hypercenterC5×C7×C13#157
commutator, hypocenterC32C4×C5×C7×C13
FrattiniC1G
Fitting, socleC32×C5×C7×C13C4
prime radicalC5×C7×C13×C3⋊D3C2
cosocleC3⋊D3C2×C5×C7×C13
LCSG ▷ C32
UCSC1 ◁ C5×C7×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

2730 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 800);