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C5×C7⋊#90865 #30655755

order16380
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C7⋊#90865
unambiguous semidirect productC7⋊(C5×#90865)

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C4
derived, HallC32×C7×C13 ⋊ C4×C5
HallC32×C5×C13 ⋊ Dic7
HallC5×C7×C13 ⋊ #157
HallC32×C5×C7 ⋊ Dic13
HallC32×C13 ⋊ C5×Dic7
HallC7×C13 ⋊ C5×#157
HallC5×C13 ⋊ C7⋊#157
HallC32×C7 ⋊ C5×Dic13
HallC32×C5 ⋊ Dic91
HallC5×C7 ⋊ #90865
SylowC13 ⋊ C5×C7⋊#157
SylowC32 ⋊ C5×Dic91
SylowC7 ⋊ C5×#90865

Subgroups

subgroupG/H
center, hypercenterC5C7⋊#90865
commutator, hypocenterC32×C7×C13C4×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C13C4
prime radicalC5×C7×C13×C3⋊D3C2
cosocleC7×C13×C3⋊D3C2×C5
LCSG ▷ C32×C7×C13
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

1380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 805);