Finite Group Databasebeta

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C7×#13049904⋊C3 #41031204

order27300
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#13049904⋊C3
unambiguous semidirect product#13049904⋊(C3×C7)

Splittings

Fitting, HallC7×C13×C25 ⋊ C3×C4
derived, HallC13×C25 ⋊ C3×C4×C7
HallC7×#13049904 ⋊ C3
HallC7×C25×C13⋊C3 ⋊ C4
Hall#13049904 ⋊ C3×C7
HallC25×C13⋊C3 ⋊ C4×C7
HallC7×C13⋊C3 ⋊ Dic25
HallC7×C25 ⋊ AGL(1,𝔽13)
HallC7×C13 ⋊ C3×Dic25
HallC13⋊C3 ⋊ C7×Dic25
SylowC25 ⋊ C7×AGL(1,𝔽13)
SylowC13 ⋊ C3×C7×Dic25

Subgroups

subgroupG/H
center, hypercenterC7#13049904⋊C3
commutator, hypocenterC13×C25C3×C4×C7
FrattiniC5C7×#63118⋊C3
FittingC7×C13×C25C3×C4
socleC5×C7×C13C3×Dic5
prime radicalC5×C7×D13⋊C3D5
cosocleC25×D13C2×C3×C7
LCSG ▷ C13×C25
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2275

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 94);