Finite Group Databasebeta

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C3×C5×C7⋊(C7⋊#261) #50304345

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C7

Aliases

direct productC3×C5×C7⋊(C7⋊#261)

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derived, HallC72×C13 ⋊ C3×C4×C5
HallC5×C72×C13 ⋊ C3×C4
HallC3×C72×C13 ⋊ C4×C5
HallC3×C5×C72 ⋊ #261
HallC5×C72 ⋊ C3×#261
HallC3×C5×C13 ⋊ C7⋊Dic7
HallC3×C72 ⋊ C5×#261
HallC5×C13 ⋊ C3×C7⋊Dic7
SylowC72 ⋊ C3×C5×#261
HallC3×C13 ⋊ C5×C7⋊Dic7
SylowC13 ⋊ C3×C5×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC3×C5C7⋊(C7⋊#261)
commutator, hypocenterC72×C13C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C5×C72×D13C2
cosocleC72×D13C2×C3×C5
LCSG ▷ C72×C13
UCSC1 ◁ C3×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

2985 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1031);