Finite Group Databasebeta

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C19×Dic455 #46829124

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

Aliases

direct productC19×Dic455
unambiguous semidirect productC7⋊(C19×Dic65)

Splittings

derived, HallC5×C7×C13 ⋊ C4×C19
HallC5×C7×C13×C19 ⋊ C4
HallC7×C13×C19 ⋊ Dic5
HallC5×C13×C19 ⋊ Dic7
HallC5×C7×C19 ⋊ Dic13
HallC13×C19 ⋊ Dic35
HallC7×C19 ⋊ Dic65
HallC5×C19 ⋊ Dic91
HallC7×C13 ⋊ C19×Dic5
HallC5×C13 ⋊ C19×Dic7
HallC5×C7 ⋊ C19×Dic13
SylowC13 ⋊ C19×Dic35
SylowC7 ⋊ C19×Dic65
SylowC5 ⋊ C19×Dic91

Subgroups

subgroupG/H
center, hypercenterC2×C19D455
commutator, hypocenterC5×C7×C13C4×C19
FrattiniC2C19×D455
Fitting, socle, prime radicalC2×C5×C7×C13×C19C2
cosocleC2×C5×C7×C13C2×C19
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34580

Conjugacy classes & character table

8702 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 15);