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C32×C5×D5×C31 #28358520

order13950
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C31 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×D5×C31
unambiguous semidirect productC5⋊(C2×C32×C5×C31)

Splittings

Fitting, socle, HallC32×C52×C31 ⋊ C2
derivedC5 ⋊ C2×C32×C5×C31
HallC52×C31 ⋊ C2×C32
HallC32×C52 ⋊ C2×C31
SylowC52 ⋊ C2×C32×C31

Subgroups

subgroupG/H
center, hypercenterC32×C5×C31D5
commutator, cosocle, hypocenterC5C2×C32×C5×C31
FrattiniC1G
Fitting, socleC32×C52×C31C2
LCSG ▷ C5
UCSC1 ◁ C32×C5×C31

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5580 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×D5×D31, C32×C5×AGL(1,𝔽5)×C31, C32×C5×C31⋊AGL(1,𝔽5), …
maximal normal subgroup ofC32×C5×D5×D31, C32×C5×AGL(1,𝔽5)×C31, C32×C5×C31⋊AGL(1,𝔽5), …
maximal quotient ofC32×C5×Dic5×C31, C2×C32×C5×D5×C31

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13950, 163);