Finite Group Databasebeta

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C2×C5×C9×D5×C31 #42124591

order27900
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C5×C9×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×D5×C31
unambiguous semidirect productC5⋊(C22×C5×C9×C31)
unambiguous semidirect product(C2×C5)⋊(C2×C5×C9×C31)

Splittings

FittingC2×C52×C9×C31 ⋊ C2
derivedC5 ⋊ C22×C5×C9×C31
HallC52×C9×C31 ⋊ C22
HallC52×C31 ⋊ C22×C9
HallC52×C9 ⋊ C22×C31
SylowC52 ⋊ C22×C9×C31

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9×C31D5
commutator, hypocenterC5C22×C5×C9×C31
FrattiniC3C2×C3×C5×D5×C31
FittingC2×C52×C9×C31C2
socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C5×D5×C31C3
cosocleC3×C5C22×C3×C5×C31
LCSG ▷ C5
UCSC1 ◁ C2×C5×C9×C31

144 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 84 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

11160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 338);