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C2×C5×D5×C13⋊C9 #26043395

order11700
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D5×C13⋊C9
unambiguous semidirect productC5⋊(C22×C5×C13⋊C9)
unambiguous semidirect product(C2×C5)⋊(C2×C5×C13⋊C9)
unambiguous semidirect product(C2×D5×C13)⋊(C5×C9)
unambiguous semidirect product(C2×C5×D5×C13)⋊C9

Splittings

derivedC5×C13 ⋊ C22×C5×C9
HallC52×C13⋊C9 ⋊ C22
HallC2×C5×D5×C13 ⋊ C9
HallC52×C13 ⋊ C22×C9
SylowC52 ⋊ C22×C13⋊C9
SylowC13 ⋊ C2×C5×C9×D5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D5×C13⋊C3
commutator, hypocenterC5×C13C22×C5×C9
FrattiniC3C2×C5×D5×C13⋊C3
Fitting, socleC2×C3×C52×C13C2×C3
prime radicalC2×C3×C5×D5×C13C3
cosocleC3×C5×C13C22×C3×C5
LCSG ▷ C5×C13
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

840 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 242);