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C5×C13×C31⋊C3 #20258371

order6045
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×C31⋊C3
unambiguous semidirect product(C5×C31)⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C13×C31 ⋊ C3
derived, SylowC31 ⋊ C3×C5×C13
HallC13×C31 ⋊ C3×C5
HallC5×C31 ⋊ C3×C13

Subgroups

subgroupG/H
center, hypercenterC5×C13C31⋊C3
commutator, hypocenterC31C3×C5×C13
FrattiniC1G
Fitting, socleC5×C13×C31C3
LCSG ▷ C31
UCSC1 ◁ C5×C13

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

845 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×C13×C31⋊C3, C5×C13×D31⋊C3, C5×D13×C31⋊C3, …
maximal normal subgroup ofC2×C5×C13×C31⋊C3, C5×C13×D31⋊C3, C5×D13×C31⋊C3, …
maximal quotient ofC2×C5×C13×C31⋊C3, C5×C13×C31⋊C9, C3×C5×C13×C31⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6045, 3);