Finite Group Databasebeta

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C3×C7⋊#13091734 #44501401

order30660
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊#13091734

Splittings

Fitting, socle, HallC3×C5×C7×C73 ⋊ C4
derived, HallC5×C7×C73 ⋊ C3×C4
HallC3×C7×C73 ⋊ AGL(1,𝔽5)
HallC3×C5×C73 ⋊ Dic7
HallC7×C73 ⋊ C3×AGL(1,𝔽5)
HallC5×C73 ⋊ C3×Dic7
HallC3×C73 ⋊ C7⋊AGL(1,𝔽5)
HallC3×C5×C7 ⋊ Dic73
SylowC73 ⋊ C3×C7⋊AGL(1,𝔽5)
HallC5×C7 ⋊ C3×Dic73
HallC3×C7 ⋊ #13091734
HallC3×C5 ⋊ Dic511
SylowC7 ⋊ C3×#13091734
SylowC5 ⋊ C3×Dic511

Subgroups

subgroupG/H
center, hypercenterC3C7⋊#13091734
commutator, hypocenterC5×C7×C73C3×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C73C4
prime radicalC3×C7×D5×C73C2
cosocleC7×D5×C73C2×C3
LCSG ▷ C5×C7×C73
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7665

Conjugacy classes & character table

3075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 164);