Finite Group Databasebeta

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C3×D5×C17×C31 #30629027

order15810
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C3×C17×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5×C17×C31
unambiguous semidirect productC5⋊(C2×C3×C17×C31)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C17×C31
HallC5×C17×C31 ⋊ C2×C3
HallC3×C5×C31 ⋊ C2×C17
HallC3×C5×C17 ⋊ C2×C31
HallC5×C31 ⋊ C2×C3×C17
HallC5×C17 ⋊ C2×C3×C31
HallC3×C5 ⋊ C2×C17×C31

Subgroups

subgroupG/H
center, hypercenterC3×C17×C31D5
commutator, cosocle, hypocenterC5C2×C3×C17×C31
FrattiniC1G
Fitting, socleC3×C5×C17×C31C2
LCSG ▷ C5
UCSC1 ◁ C3×C17×C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

6324 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C17×AGL(1,𝔽5)×C31, C3×C17×C31⋊AGL(1,𝔽5), C3×C31×#66774, …
maximal normal subgroup ofC3×C17×AGL(1,𝔽5)×C31, C3×C17×C31⋊AGL(1,𝔽5), C3×C31×#66774, …
maximal quotient ofC3×C17×Dic5×C31, C2×C3×D5×C17×C31

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 8);