Finite Group Databasebeta

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C2×C5×C17×C31⋊C3 #30629022

order15810
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C17×C31⋊C3
unambiguous semidirect product(C2×C5×C31)⋊(C3×C17)
unambiguous semidirect product(C2×C5×C17×C31)⋊C3

Splittings

Fitting, socle, HallC2×C5×C17×C31 ⋊ C3
derived, SylowC31 ⋊ C2×C3×C5×C17
HallC5×C17×C31 ⋊ C2×C3
HallC2×C17×C31 ⋊ C3×C5
HallC17×C31 ⋊ C2×C3×C5
HallC2×C5×C31 ⋊ C3×C17
HallC5×C31 ⋊ C2×C3×C17
HallC2×C31 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17C31⋊C3
commutator, cosocle, hypocenterC31C2×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C5×C17×C31C3
LCSG ▷ C31
UCSC1 ◁ C2×C5×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5270

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C17×C31⋊C3, C5×C17×(C31⋊C3)⋊C4, C5×Dic17×C31⋊C3, …
maximal normal subgroup ofC4×C5×C17×C31⋊C3, C5×C17×(C31⋊C3)⋊C4, C5×Dic17×C31⋊C3, …
maximal quotient ofC4×C5×C17×C31⋊C3, C22×C5×C17×C31⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 3);