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C13×C17×C7⋊AGL(1,𝔽5) #44525903

order30940
automorphism?
homologyAbelianization (H1) = C4×C13×C17 · Schur multiplier (H2) = C1

Aliases

direct productC13×C17×C7⋊AGL(1,𝔽5)
unambiguous semidirect productC7⋊(C13×C17×AGL(1,𝔽5))

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC13×C17C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C13×C17
FrattiniC1G
Fitting, socleC5×C7×C13×C17C4
prime radicalC7×D5×C13×C17C2
cosocleC7×D5C2×C13×C17
LCSG ▷ C5×C7
UCSC1 ◁ C13×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

3757 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 53);