Finite Group Databasebeta

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C5×#16840861 #34086134

order19530
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×#16840861

Splittings

derived, HallC7×C31 ⋊ C2×C5×C9
HallC5×#14519870 ⋊ C2
HallC5×D7×C31 ⋊ C9
Hall#14519870 ⋊ C2×C5
HallC5×C7×C31 ⋊ C2×C9
HallD7×C31 ⋊ C5×C9
HallC5×C31 ⋊ D7⋊C9
HallC5×D7 ⋊ C31⋊C9
HallC5×C7 ⋊ C2×C31⋊C9
SylowC31 ⋊ C5×D7⋊C9
HallD7 ⋊ C5×C31⋊C9
SylowC7 ⋊ C2×C5×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5#13049959
commutator, hypocenterC7×C31C2×C5×C9
FrattiniC3C5×#13049959
Fitting, socleC3×C5×C7×C31C2×C3
prime radicalC3×C5×D7×C31C3
cosocleC3×C7×C31C2×C3×C5
LCSG ▷ C7×C31
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9765

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 39);