Finite Group Databasebeta

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C7×C3⋊(C3⋊#66775) #36339537

order21420
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×C3⋊(C3⋊#66775)
unambiguous semidirect productC3⋊(C7×C3⋊#66775)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C4
derived, HallC32×C5×C17 ⋊ C4×C7
HallC32×C7×C17 ⋊ AGL(1,𝔽5)
HallC5×C7×C17 ⋊ C3⋊Dic3
HallC32×C5×C7 ⋊ #595
HallC32×C17 ⋊ C7×AGL(1,𝔽5)
HallC7×C17 ⋊ C3⋊ΓL(1,𝔽16)
HallC5×C17 ⋊ C7×C3⋊Dic3
HallC32×C7 ⋊ #66775
HallC32×C5 ⋊ C7×#595
HallC5×C7 ⋊ C3⋊(C3⋊#595)
SylowC17 ⋊ C7×C3⋊ΓL(1,𝔽16)
SylowC32 ⋊ C7×#66775
SylowC5 ⋊ C7×C3⋊(C3⋊#595)

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C3⋊#66775)
commutator, hypocenterC32×C5×C17C4×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C17C4
prime radicalC32×C7×D85C2
cosocleC32×D85C2×C7
LCSG ▷ C32×C5×C17
UCSC1 ◁ C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

1407 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 369);