Finite Group Databasebeta

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C7×C3⋊#13091734 #44501421

order30660
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊#13091734
unambiguous semidirect productC3⋊(C7×#13091734)

Splittings

Fitting, socle, HallC3×C5×C7×C73 ⋊ C4
derived, HallC3×C5×C73 ⋊ C4×C7
HallC5×C7×C73 ⋊ Dic3
HallC3×C7×C73 ⋊ AGL(1,𝔽5)
HallC7×C73 ⋊ ΓL(1,𝔽16)
HallC5×C73 ⋊ C7×Dic3
HallC3×C73 ⋊ C7×AGL(1,𝔽5)
HallC3×C5×C7 ⋊ Dic73
SylowC73 ⋊ C7×ΓL(1,𝔽16)
HallC5×C7 ⋊ Dic219
HallC3×C7 ⋊ #13091734
HallC3×C5 ⋊ C7×Dic73
SylowC5 ⋊ C7×Dic219
SylowC3 ⋊ C7×#13091734

Subgroups

subgroupG/H
center, hypercenterC7C3⋊#13091734
commutator, hypocenterC3×C5×C73C4×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C73C4
prime radicalC3×C7×D5×C73C2
cosocleC3×D5×C73C2×C7
LCSG ▷ C3×C5×C73
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7665

Conjugacy classes & character table

3087 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 184);