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C2×(C5⋊D5)⋊(C31⋊C9) #42124531

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

Aliases

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

Splittings

derived, HallC52×C31 ⋊ C22×C9
HallC52⋊(C31⋊C9) ⋊ C22
HallC2×C31×C5⋊D5 ⋊ C9
HallC2×C5⋊D5 ⋊ C31⋊C9
SylowC31 ⋊ C2×(C5⋊D5)⋊C9
SylowC52 ⋊ C22×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3(C5⋊D5)⋊(C31⋊C3)
commutator, hypocenterC52×C31C22×C9
FrattiniC3C2×(C5⋊D5)⋊(C31⋊C3)
Fitting, socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C31×C5⋊D5C3
cosocleC3×C52×C31C22×C3
LCSG ▷ C52×C31
UCSC1 ◁ C2×C3

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

900 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 278);