Finite Group Databasebeta

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C3×C7⋊#13049908 #41031272

order27300
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊#13049908

Splittings

Fitting, HallC3×C7×C13×C25 ⋊ C4
derived, HallC7×C13×C25 ⋊ C3×C4
HallC3×C13×C25 ⋊ Dic7
HallC3×C7×C25 ⋊ #261
HallC13×C25 ⋊ C3×Dic7
HallC3×C7×C13 ⋊ #1035
HallC7×C25 ⋊ C3×#261
HallC7×C13 ⋊ C3×#1035
HallC3×C25 ⋊ C7⋊#261
HallC3×C13 ⋊ C7⋊#1035
SylowC25 ⋊ C3×C7⋊#261
HallC3×C7 ⋊ #13049908
SylowC13 ⋊ C3×C7⋊#1035
SylowC7 ⋊ C3×#13049908

Subgroups

subgroupG/H
center, hypercenterC3C7⋊#13049908
commutator, hypocenterC7×C13×C25C3×C4
FrattiniC5C3×C7⋊#63122
FittingC3×C7×C13×C25C4
socleC3×C5×C7×C13AGL(1,𝔽5)
prime radicalC3×C7×D325C2
cosocleC7×D325C2×C3
LCSG ▷ C7×C13×C25
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6825

Conjugacy classes & character table

1731 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 162);