Finite Group Databasebeta

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C2×C5⋊(C5⋊(D31⋊C9)) #42124525

order27900
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5⋊(C5⋊(D31⋊C9))
unambiguous semidirect product(C2×C5)⋊(C5⋊(D31⋊C9))
unambiguous semidirect product(C2×C31⋊C9)⋊(C5⋊D5)

Splittings

derived, HallC52×C31 ⋊ C22×C9
HallC52×C31⋊C9 ⋊ C22
HallC2×C5⋊D155 ⋊ C9
HallC31⋊C9 ⋊ C2×C5⋊D5
SylowC31 ⋊ C2×C9×C5⋊D5
SylowC52 ⋊ C2×D31⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(C5⋊(D31⋊C3))
commutator, hypocenterC52×C31C22×C9
FrattiniC3C2×C5⋊(C5⋊(D31⋊C3))
Fitting, socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C5⋊D155C3
cosocleC3×C52×C31C22×C3
LCSG ▷ C52×C31
UCSC1 ◁ C2×C3

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1002 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 272);