Finite Group Databasebeta

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C2×C25×D31⋊C9 #42124284

order27900
automorphism?
homologyAbelianization (H1) = C22×C9×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×D31⋊C9
unambiguous semidirect product(C2×C25×D31)⋊C9

Splittings

derived, SylowC31 ⋊ C22×C9×C25
HallC25×C31⋊C9 ⋊ C22
HallC2×C25×D31 ⋊ C9
HallC25×C31 ⋊ C22×C9
HallC31⋊C9 ⋊ C22×C25
HallC2×D31 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D31⋊C3
commutator, hypocenterC31C22×C9×C25
FrattiniC3×C5C2×C5×D31⋊C3
FittingC2×C3×C25×C31C2×C3
socleC2×C3×C5×C31C2×C3×C5
prime radicalC2×C3×C5×D31C3×C5
cosocleC3×C5×C31C22×C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C3×C25

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 31);