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C13×C7⋊#66775 #44525904

order30940
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C7⋊#66775
unambiguous semidirect productC7⋊(C13×#66775)

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C4
derived, HallC5×C7×C17 ⋊ C4×C13
HallC7×C13×C17 ⋊ AGL(1,𝔽5)
HallC5×C13×C17 ⋊ Dic7
HallC5×C7×C13 ⋊ #595
HallC13×C17 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C17 ⋊ C13×AGL(1,𝔽5)
HallC7×C13 ⋊ #66775
HallC5×C17 ⋊ C13×Dic7
HallC5×C13 ⋊ C7⋊#595
HallC5×C7 ⋊ C13×#595
SylowC17 ⋊ C13×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C13×#66775
SylowC5 ⋊ C13×C7⋊#595

Subgroups

subgroupG/H
center, hypercenterC13C7⋊#66775
commutator, hypocenterC5×C7×C17C4×C13
FrattiniC1G
Fitting, socleC5×C7×C13×C17C4
prime radicalC7×C13×D85C2
cosocleC7×D85C2×C13
LCSG ▷ C5×C7×C17
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

2041 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 54);