Finite Group Databasebeta

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C5×C3⋊(C7⋊#64408) #44501412

order30660
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(C7⋊#64408)
unambiguous semidirect productC3⋊(C5×C7⋊#64408)
unambiguous semidirect productC7⋊(C5×C3⋊#64408)

Splittings

Fitting, socle, HallC3×C5×C7×C73 ⋊ C4
derived, HallC3×C7×C73 ⋊ C4×C5
HallC5×C7×C73 ⋊ Dic3
HallC3×C5×C73 ⋊ Dic7
HallC7×C73 ⋊ C5×Dic3
HallC5×C73 ⋊ Dic21
HallC3×C73 ⋊ C5×Dic7
HallC3×C5×C7 ⋊ #64408
SylowC73 ⋊ C5×Dic21
HallC5×C7 ⋊ C3⋊#64408
HallC3×C7 ⋊ C5×#64408
HallC3×C5 ⋊ C7⋊#64408
SylowC7 ⋊ C5×C3⋊#64408
SylowC3 ⋊ C5×C7⋊#64408

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C7⋊#64408)
commutator, hypocenterC3×C7×C73C4×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C73C4
prime radicalC3×C5×C7×D73C2
cosocleC3×C7×D73C2×C5
LCSG ▷ C3×C7×C73
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7665

Conjugacy classes & character table

2010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 175);