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C7×#14556844 #30655759

order16380
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×#14556844

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C4
derived, HallC32×C5×C13 ⋊ C4×C7
HallC32×C7×C13 ⋊ AGL(1,𝔽5)
HallC5×C7×C13 ⋊ #157
HallC32×C5×C7 ⋊ Dic13
HallC32×C13 ⋊ C7×AGL(1,𝔽5)
HallC7×C13 ⋊ #4380
HallC5×C13 ⋊ C7×#157
HallC32×C7 ⋊ #63120
HallC32×C5 ⋊ C7×Dic13
HallC5×C7 ⋊ #90865
SylowC13 ⋊ C7×#4380
SylowC32 ⋊ C7×#63120
SylowC5 ⋊ C7×#90865

Subgroups

subgroupG/H
center, hypercenterC7#14556844
commutator, hypocenterC32×C5×C13C4×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C13C4
prime radicalC7×C13×C3⋊D15C2
cosocleC13×C3⋊D15C2×C7
LCSG ▷ C32×C5×C13
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

1113 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 809);