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C7×C3⋊#13049908 #41031292

order27300
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊#13049908
unambiguous semidirect productC3⋊(C7×#13049908)

Splittings

Fitting, HallC3×C7×C13×C25 ⋊ C4
derived, HallC3×C13×C25 ⋊ C4×C7
HallC7×C13×C25 ⋊ Dic3
HallC3×C7×C25 ⋊ #261
HallC13×C25 ⋊ C7×Dic3
HallC3×C7×C13 ⋊ #1035
HallC7×C25 ⋊ C3⋊#261
HallC7×C13 ⋊ C3⋊#1035
HallC3×C25 ⋊ C7×#261
HallC3×C13 ⋊ C7×#1035
SylowC25 ⋊ C7×C3⋊#261
HallC3×C7 ⋊ #13049908
SylowC13 ⋊ C7×C3⋊#1035
SylowC3 ⋊ C7×#13049908

Subgroups

subgroupG/H
center, hypercenterC7C3⋊#13049908
commutator, hypocenterC3×C13×C25C4×C7
FrattiniC5C7×C3⋊#63122
FittingC3×C7×C13×C25C4
socleC3×C5×C7×C13AGL(1,𝔽5)
prime radicalC3×C7×D325C2
cosocleC3×D325C2×C7
LCSG ▷ C3×C13×C25
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6825

Conjugacy classes & character table

1743 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 182);