Finite Group Databasebeta

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C3×D5×#11715913 #37552086

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

Aliases

direct productC3×D5×#11715913
unambiguous semidirect productC5⋊(C2×C3×#11715913)

Splittings

Fitting, socleC3×C5×C7×C37 ⋊ C2×C3
derived, HallC5×C7×C37 ⋊ C2×C32
HallC3×C5×#11715913 ⋊ C2
HallC7×D5×C37 ⋊ C32
HallD5×C37 ⋊ C3×ΓL(1,𝔽8)
HallC7×C37 ⋊ C32×D5
HallC5×C37 ⋊ C2×C3×ΓL(1,𝔽8)
HallC7×D5 ⋊ C3×C37⋊C3
SylowC37 ⋊ C3×D5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×C37⋊C3
SylowC7 ⋊ C3×D5×C37⋊C3
SylowC5 ⋊ C2×C3×#11715913

Subgroups

subgroupG/H
center, hypercenterC3D5×#11715913
commutator, cosocle, hypocenterC5×C7×C37C2×C32
FrattiniC1G
Fitting, socleC3×C5×C7×C37C2×C3
LCSG ▷ C5×C7×C37
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3885

Conjugacy classes & character table

1068 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 105);