Finite Group Databasebeta

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C19×Dic5×C31⋊C3 #47977573

order35340
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×Dic5×C31⋊C3
unambiguous semidirect product(Dic5×C31)⋊(C3×C19)

Splittings

derived, HallC5×C31 ⋊ C3×C4×C19
HallC19×Dic5×C31 ⋊ C3
HallC5×C19×C31⋊C3 ⋊ C4
HallC5×C19×C31 ⋊ C3×C4
HallDic5×C31 ⋊ C3×C19
HallC19×C31 ⋊ C3×Dic5
HallC5×C31⋊C3 ⋊ C4×C19
HallC5×C19 ⋊ C4×C31⋊C3
SylowC31 ⋊ C3×C19×Dic5
SylowC5 ⋊ C4×C19×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C19D5×C31⋊C3
commutator, hypocenterC5×C31C3×C4×C19
FrattiniC2D5×C19×C31⋊C3
Fitting, socleC2×C5×C19×C31C2×C3
prime radicalC2×C5×C19×C31⋊C3C2
cosocleC2×C5×C31C2×C3×C19
LCSG ▷ C5×C31
UCSC1 ◁ C2×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11780

Conjugacy classes & character table

1976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 45);