Finite Group Databasebeta

← Prev (#42124515) Next (#42124517) →

C2×C9×C5⋊(D31⋊C5) #42124516

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

Aliases

direct productC2×C9×C5⋊(D31⋊C5)
unambiguous semidirect product(C2×C5)⋊(C9×D31⋊C5)
unambiguous semidirect product(C2×C9×D155)⋊C5

Splittings

FittingC2×C5×C9×C31 ⋊ C2×C5
derivedC5×C31 ⋊ C22×C5×C9
HallC5×C9×ΓL(1,𝔽32) ⋊ C22
HallC5×ΓL(1,𝔽32) ⋊ C22×C9
HallC9×C31 ⋊ C2×C5×D5
SylowC31 ⋊ C2×C5×C9×D5

Subgroups

subgroupG/H
center, hypercenterC2×C9C5⋊(D31⋊C5)
commutator, hypocenterC5×C31C22×C5×C9
FrattiniC3C2×C3×C5⋊(D31⋊C5)
FittingC2×C5×C9×C31C2×C5
socleC2×C3×C5×C31C2×C3×C5
prime radicalC2×C3×C5⋊(D31⋊C5)C3
cosocleC3×C5×C31C22×C3×C5
LCSG ▷ C5×C31
UCSC1 ◁ C2×C9

144 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

630 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 263);