Finite Group Databasebeta

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C2×C32×C5×D31⋊C5 #42124822

order27900
isoclinismisoclinic class of D31⋊C5
automorphism?
homologyAbelianization (H1) = C22×C32×C52 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC2×C32×C5×D31⋊C5
unambiguous semidirect product(C2×C32×D31)⋊C52
unambiguous semidirect product(C2×C32×C5×D31)⋊C5

Splittings

Fitting, socleC2×C32×C5×C31 ⋊ C2×C5
derived, SylowC31 ⋊ C22×C32×C52
HallC32×C5×ΓL(1,𝔽32) ⋊ C22
HallC2×C32×D31 ⋊ C52
HallC5×ΓL(1,𝔽32) ⋊ C22×C32
HallC32×C31 ⋊ C22×C52
HallC2×D31 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D31⋊C5
commutator, cosocle, hypocenterC31C22×C32×C52
FrattiniC1G
Fitting, socleC2×C32×C5×C31C2×C5
LCSG ▷ C31
UCSC1 ◁ C2×C32×C5

480 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 569);