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C2×C9⋊(D31⋊C25) #42124283

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

Aliases

direct productC2×C9⋊(D31⋊C25)
unambiguous semidirect product(C2×C9)⋊(D31⋊C25)
unambiguous semidirect product(C2×D279)⋊C25
unambiguous semidirect product(C2×C31⋊C25)⋊D9

Splittings

derived, HallC9×C31 ⋊ C22×C25
HallC9×C31⋊C25 ⋊ C22
HallC2×D279 ⋊ C25
HallC31⋊C25 ⋊ C2×D9
SylowC31 ⋊ C2×D9×C25
SylowC9 ⋊ C2×D31⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5C9⋊(D31⋊C5)
commutator, hypocenterC9×C31C22×C25
FrattiniC3×C5C2×C3⋊(D31⋊C5)
FittingC2×C5×C9×C31C2×C5
socleC2×C3×C5×C31C5×D3
prime radicalC2×C5×D279C5
cosocleC5×C9×C31C22×C5
LCSG ▷ C9×C31
UCSC1 ◁ C2×C5

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 30);