Finite Group Databasebeta

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C2×C9×D31⋊C25 #42124281

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

Aliases

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

Splittings

derived, SylowC31 ⋊ C22×C9×C25
HallC9×C31⋊C25 ⋊ C22
HallC2×C9×D31 ⋊ C25
HallC31⋊C25 ⋊ C22×C9
HallC9×C31 ⋊ C22×C25
HallC2×D31 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D31⋊C5
commutator, hypocenterC31C22×C9×C25
FrattiniC3×C5C2×C3×D31⋊C5
FittingC2×C5×C9×C31C2×C5
socleC2×C3×C5×C31C2×C3×C5
prime radicalC2×C3×C5×D31C3×C5
cosocleC3×C5×C31C22×C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C5×C9

90 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, 28);