Finite Group Databasebeta

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C7×#13091734⋊C3 #44501301

order30660
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC5×C7×C73 ⋊ C3×C4
derived, HallC5×C73 ⋊ C3×C4×C7
HallC7×#13091734 ⋊ C3
HallC5×C7×C73⋊C3 ⋊ C4
HallC7×C73⋊C3 ⋊ AGL(1,𝔽5)
Hall#13091734 ⋊ C3×C7
HallC5×C73⋊C3 ⋊ C4×C7
HallC7×C73 ⋊ C3×AGL(1,𝔽5)
HallC73⋊C3 ⋊ C7×AGL(1,𝔽5)
SylowC73 ⋊ C3×C7×AGL(1,𝔽5)
HallC5×C7 ⋊ Dic73⋊C3
SylowC5 ⋊ C7×Dic73⋊C3

Subgroups

subgroupG/H
center, hypercenterC7#13091734⋊C3
commutator, hypocenterC5×C73C3×C4×C7
FrattiniC1G
Fitting, socleC5×C7×C73C3×C4
prime radicalC7×D5×C73⋊C3C2
cosocleD5×C73C2×C3×C7
LCSG ▷ C5×C73
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2555

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 64);