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C13×C7⋊(C19⋊AGL(1,𝔽5)) #46829147

order34580
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C7⋊(C19⋊AGL(1,𝔽5))
unambiguous semidirect productC7⋊(C13×C19⋊AGL(1,𝔽5))
unambiguous semidirect productC19⋊(C13×C7⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC5×C7×C13×C19 ⋊ C4
derived, HallC5×C7×C19 ⋊ C4×C13
HallC7×C13×C19 ⋊ AGL(1,𝔽5)
HallC5×C13×C19 ⋊ Dic7
HallC5×C7×C13 ⋊ Dic19
HallC13×C19 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C19 ⋊ C13×AGL(1,𝔽5)
HallC5×C19 ⋊ C13×Dic7
HallC7×C13 ⋊ C19⋊AGL(1,𝔽5)
HallC5×C13 ⋊ Dic133
HallC5×C7 ⋊ C13×Dic19
SylowC19 ⋊ C13×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C13×C19⋊AGL(1,𝔽5)
SylowC5 ⋊ C13×Dic133

Subgroups

subgroupG/H
center, hypercenterC13C7⋊(C19⋊AGL(1,𝔽5))
commutator, hypocenterC5×C7×C19C4×C13
FrattiniC1G
Fitting, socleC5×C7×C13×C19C4
prime radicalC7×D5×C13×C19C2
cosocleC7×D5×C19C2×C13
LCSG ▷ C5×C7×C19
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8645

Conjugacy classes & character table

3497 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 38);