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C19×C7⋊#63121 #46829150

order34580
automorphism?
homologyAbelianization (H1) = C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C7⋊#63121
unambiguous semidirect productC7⋊(C19×#63121)

Splittings

Fitting, socle, HallC5×C7×C13×C19 ⋊ C4
derived, HallC5×C7×C13 ⋊ C4×C19
HallC7×C13×C19 ⋊ AGL(1,𝔽5)
HallC5×C13×C19 ⋊ Dic7
HallC5×C7×C19 ⋊ #261
HallC13×C19 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C19 ⋊ #63121
HallC5×C19 ⋊ C7⋊#261
HallC7×C13 ⋊ C19×AGL(1,𝔽5)
HallC5×C13 ⋊ C19×Dic7
HallC5×C7 ⋊ C19×#261
SylowC13 ⋊ C19×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C19×#63121
SylowC5 ⋊ C19×C7⋊#261

Subgroups

subgroupG/H
center, hypercenterC19C7⋊#63121
commutator, hypocenterC5×C7×C13C4×C19
FrattiniC1G
Fitting, socleC5×C7×C13×C19C4
prime radicalC7×C19×D65C2
cosocleC7×D65C2×C19
LCSG ▷ C5×C7×C13
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8645

Conjugacy classes & character table

2318 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 41);