Finite Group Databasebeta

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C2×D25×C31⋊C9 #42124285

order27900
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×D25×C31⋊C9
unambiguous semidirect productC25⋊(C22×C31⋊C9)
unambiguous semidirect product(C2×C25)⋊(C2×C31⋊C9)
unambiguous semidirect product(C2×C31×D25)⋊C9

Splittings

derived, HallC25×C31 ⋊ C22×C9
HallC25×C31⋊C9 ⋊ C22
HallC2×C31×D25 ⋊ C9
SylowC31 ⋊ C2×C9×D25
SylowC25 ⋊ C22×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3D25×C31⋊C3
commutator, hypocenterC25×C31C22×C9
FrattiniC3×C5C2×D5×C31⋊C3
FittingC2×C3×C25×C31C2×C3
socleC2×C3×C5×C31C3×D5
prime radicalC2×C3×C31×D25C3
cosocleC3×C25×C31C22×C3
LCSG ▷ C25×C31
UCSC1 ◁ C2×C3

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 32);