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C5×(C31⋊C3)⋊Dic19 #47977569

order35340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C31⋊C3)⋊Dic19

Splittings

derived, HallC19×C31 ⋊ C3×C4×C5
HallC5×Dic589 ⋊ C3
HallC5×C19×C31⋊C3 ⋊ C4
HallC5×C19×C31 ⋊ C3×C4
HallDic589 ⋊ C3×C5
HallC19×C31⋊C3 ⋊ C4×C5
HallC5×C31⋊C3 ⋊ Dic19
HallC5×C31 ⋊ C3×Dic19
HallC5×C19 ⋊ (C31⋊C3)⋊C4
HallC31⋊C3 ⋊ C5×Dic19
SylowC31 ⋊ C3×C5×Dic19
SylowC19 ⋊ C5×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5(C31⋊C3)⋊D19
commutator, hypocenterC19×C31C3×C4×C5
FrattiniC2C5×(C31⋊C3)⋊D19
Fitting, socleC2×C5×C19×C31C2×C3
prime radicalC2×C5×C19×C31⋊C3C2
cosocleC2×C19×C31C2×C3×C5
LCSG ▷ C19×C31
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11780

Conjugacy classes & character table

1280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 41);