Finite Group Databasebeta

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C7×C19×#63120 #46829144

order34580
automorphism?
homologyAbelianization (H1) = C4×C7×C19 · Schur multiplier (H2) = C1

Aliases

direct productC7×C19×#63120

Splittings

Fitting, socle, HallC5×C7×C13×C19 ⋊ C4
derived, HallC5×C13 ⋊ C4×C7×C19
HallC7×C13×C19 ⋊ AGL(1,𝔽5)
HallC5×C13×C19 ⋊ C4×C7
HallC5×C7×C19 ⋊ Dic13
HallC5×C7×C13 ⋊ C4×C19
HallC13×C19 ⋊ C7×AGL(1,𝔽5)
HallC5×C19 ⋊ C7×Dic13
HallC7×C13 ⋊ C19×AGL(1,𝔽5)
HallC5×C7 ⋊ C19×Dic13
SylowC13 ⋊ C7×C19×AGL(1,𝔽5)
SylowC5 ⋊ C7×C19×Dic13

Subgroups

subgroupG/H
center, hypercenterC7×C19#63120
commutator, hypocenterC5×C13C4×C7×C19
FrattiniC1G
Fitting, socleC5×C7×C13×C19C4
prime radicalC7×D5×C13×C19C2
cosocleD5×C13C2×C7×C19
LCSG ▷ C5×C13
UCSC1 ◁ C7×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8645

Conjugacy classes & character table

3857 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 35);