Finite Group Databasebeta

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C2×C5×D5×C31⋊C9 #42124524

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

Aliases

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

Splittings

derivedC5×C31 ⋊ C22×C5×C9
HallC52×C31⋊C9 ⋊ C22
HallC2×C5×D5×C31 ⋊ C9
HallC52×C31 ⋊ C22×C9
SylowC31 ⋊ C2×C5×C9×D5
SylowC52 ⋊ C22×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D5×C31⋊C3
commutator, hypocenterC5×C31C22×C5×C9
FrattiniC3C2×C5×D5×C31⋊C3
Fitting, socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C5×D5×C31C3
cosocleC3×C5×C31C22×C3×C5
LCSG ▷ C5×C31
UCSC1 ◁ C2×C3×C5

144 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 70 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

1560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 271);