Finite Group Databasebeta

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C2×C5×C9×D31⋊C5 #42124515

order27900
isoclinismisoclinic class of D31⋊C5
automorphism?
homologyAbelianization (H1) = C22×C52×C9 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5×C9×D31⋊C5
unambiguous semidirect product(C2×C9×D31)⋊C52
unambiguous semidirect product(C2×C5×C9×D31)⋊C5

Splittings

FittingC2×C5×C9×C31 ⋊ C2×C5
derived, SylowC31 ⋊ C22×C52×C9
HallC5×C9×ΓL(1,𝔽32) ⋊ C22
HallC2×C9×D31 ⋊ C52
HallC5×ΓL(1,𝔽32) ⋊ C22×C9
HallC9×C31 ⋊ C22×C52
HallC2×D31 ⋊ C52×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D31⋊C5
commutator, hypocenterC31C22×C52×C9
FrattiniC3C2×C3×C5×D31⋊C5
FittingC2×C5×C9×C31C2×C5
socleC2×C3×C5×C31C2×C3×C5
prime radicalC2×C3×C5×D31⋊C5C3
cosocleC3×C31C22×C3×C52
LCSG ▷ C31
UCSC1 ◁ C2×C5×C9

240 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, 262);