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C7×C19⋊#63118 #46829156

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

Aliases

direct productC7×C19⋊#63118
unambiguous semidirect productC19⋊(C7×#63118)

Splittings

Fitting, socle, HallC5×C7×C13×C19 ⋊ C4
derived, HallC5×C13×C19 ⋊ C4×C7
HallC7×C13×C19 ⋊ Dic5
HallC5×C7×C19 ⋊ #261
HallC5×C7×C13 ⋊ Dic19
HallC13×C19 ⋊ C7×Dic5
HallC7×C19 ⋊ #63118
HallC5×C19 ⋊ C7×#261
HallC7×C13 ⋊ Dic95
HallC5×C13 ⋊ C7×Dic19
HallC5×C7 ⋊ C19⋊#261
SylowC19 ⋊ C7×#63118
SylowC13 ⋊ C7×Dic95
SylowC5 ⋊ C7×C19⋊#261

Subgroups

subgroupG/H
center, hypercenterC7C19⋊#63118
commutator, hypocenterC5×C13×C19C4×C7
FrattiniC1G
Fitting, socleC5×C7×C13×C19C4
prime radicalC5×C7×C19×D13C2
cosocleC5×C19×D13C2×C7
LCSG ▷ C5×C13×C19
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8645

Conjugacy classes & character table

2681 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 47);