Finite Group Databasebeta

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C13×C3⋊(C7⋊#1035) #41031295

order27300
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊(C7⋊#1035)
unambiguous semidirect productC3⋊(C13×C7⋊#1035)
unambiguous semidirect productC7⋊(C13×C3⋊#1035)

Splittings

Fitting, HallC3×C7×C13×C25 ⋊ C4
derived, HallC3×C7×C25 ⋊ C4×C13
HallC7×C13×C25 ⋊ Dic3
HallC3×C13×C25 ⋊ Dic7
HallC13×C25 ⋊ Dic21
HallC3×C7×C13 ⋊ #1035
HallC7×C25 ⋊ Dic3×C13
HallC7×C13 ⋊ C3⋊#1035
HallC3×C25 ⋊ C13×Dic7
HallC3×C13 ⋊ C7⋊#1035
SylowC25 ⋊ C13×Dic21
HallC3×C7 ⋊ C13×#1035
SylowC7 ⋊ C13×C3⋊#1035
SylowC3 ⋊ C13×C7⋊#1035

Subgroups

subgroupG/H
center, hypercenterC13C3⋊(C7⋊#1035)
commutator, hypocenterC3×C7×C25C4×C13
FrattiniC5C13×C3⋊(C7⋊AGL(1,𝔽5))
FittingC3×C7×C13×C25C4
socleC3×C5×C7×C13AGL(1,𝔽5)
prime radicalC3×C7×C13×D25C2
cosocleC3×C7×D25C2×C13
LCSG ▷ C3×C7×C25
UCSC1 ◁ C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6825

Conjugacy classes & character table

1950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 185);