Finite Group Databasebeta

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C5×#20296620 #47977572

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

Aliases

direct productC5×#20296620

Splittings

derived, HallC19×C31 ⋊ C3×C4×C5
HallC5×Dic589 ⋊ C3
HallC5×#13183714 ⋊ C4
HallC5×C19×C31 ⋊ C3×C4
HallDic589 ⋊ C3×C5
Hall#13183714 ⋊ C4×C5
HallC5×C31 ⋊ (C19⋊C3)⋊C4
HallC5×C19 ⋊ (C31⋊C3)⋊C4
SylowC31 ⋊ C5×(C19⋊C3)⋊C4
SylowC19 ⋊ C5×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5#16812976
commutator, hypocenterC19×C31C3×C4×C5
FrattiniC2C5×#16812976
Fitting, socleC2×C5×C19×C31C2×C3
prime radicalC2×C5×#13183714C2
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

1040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 44);