Finite Group Databasebeta

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C3×C5×C7⋊#64408 #44501392

order30660
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7⋊#64408

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C5C7⋊#64408
commutator, hypocenterC7×C73C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C73C4
prime radicalC3×C5×C7×D73C2
cosocleC7×D73C2×C3×C5
LCSG ▷ C7×C73
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7665

Conjugacy classes & character table

2040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 155);