Finite Group Databasebeta

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C3×C5×#13095536 #37552068

order23310
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×#13095536

Splittings

Fitting, socleC3×C5×C7×C37 ⋊ C2×C3
derived, HallC7×C37 ⋊ C2×C32×C5
HallC3×C5×#11715912 ⋊ C2
HallC5×D7×C37 ⋊ C32
HallC3×#11715912 ⋊ C2×C5
HallC5×C7×C37 ⋊ C2×C32
HallD7×C37 ⋊ C32×C5
HallC5×C37 ⋊ C3×AGL(1,𝔽7)
HallC5×D7 ⋊ C3×C37⋊C3
SylowC37 ⋊ C3×C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×C37⋊C3
HallD7 ⋊ C3×C5×C37⋊C3
SylowC7 ⋊ C2×C3×C5×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5#13095536
commutator, cosocle, hypocenterC7×C37C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C37C2×C3
LCSG ▷ C7×C37
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3885

Conjugacy classes & character table

1005 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 87);