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C13×C3⋊(C7⋊(C7⋊AGL(1,𝔽5))) #50304423

order38220
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C7

Aliases

direct productC13×C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))
unambiguous semidirect productC3⋊(C13×C7⋊(C7⋊AGL(1,𝔽5)))
unambiguous semidirect productC7⋊(C13×C3⋊(C7⋊AGL(1,𝔽5)))

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derived, HallC3×C5×C72 ⋊ C4×C13
HallC5×C72×C13 ⋊ Dic3
HallC3×C72×C13 ⋊ AGL(1,𝔽5)
HallC72×C13 ⋊ ΓL(1,𝔽16)
HallC5×C72 ⋊ Dic3×C13
HallC3×C5×C13 ⋊ C7⋊Dic7
HallC3×C72 ⋊ C13×AGL(1,𝔽5)
HallC5×C13 ⋊ C3⋊(C7⋊Dic7)
SylowC72 ⋊ C13×ΓL(1,𝔽16)
HallC3×C13 ⋊ C7⋊(C7⋊AGL(1,𝔽5))
HallC3×C5 ⋊ C13×C7⋊Dic7
SylowC5 ⋊ C13×C3⋊(C7⋊Dic7)
SylowC3 ⋊ C13×C7⋊(C7⋊AGL(1,𝔽5))

Subgroups

subgroupG/H
center, hypercenterC13C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))
commutator, hypocenterC3×C5×C72C4×C13
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C72×D5×C13C2
cosocleC3×C72×D5C2×C13
LCSG ▷ C3×C5×C72
UCSC1 ◁ C13

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

3861 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1109);