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C19×C7⋊#63120 #46829152

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

Aliases

direct productC19×C7⋊#63120
unambiguous semidirect productC7⋊(C19×#63120)

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 ⋊ Dic13
HallC13×C19 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C19 ⋊ #63120
HallC5×C19 ⋊ Dic91
HallC7×C13 ⋊ C19×AGL(1,𝔽5)
HallC5×C13 ⋊ C19×Dic7
HallC5×C7 ⋊ C19×Dic13
SylowC13 ⋊ C19×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C19×#63120
SylowC5 ⋊ C19×Dic91

Subgroups

subgroupG/H
center, hypercenterC19C7⋊#63120
commutator, hypocenterC5×C7×C13C4×C19
FrattiniC1G
Fitting, socleC5×C7×C13×C19C4
prime radicalC7×D5×C13×C19C2
cosocleC7×D5×C13C2×C19
LCSG ▷ C5×C7×C13
UCSC1 ◁ C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8645

Conjugacy classes & character table

3515 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 43);