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C2×C5×C5⋊(D13⋊C9) #26043394

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

Aliases

direct productC2×C5×C5⋊(D13⋊C9)
unambiguous semidirect product(C2×C5)⋊(C5×D13⋊C9)
unambiguous semidirect product(C2×C13⋊C9)⋊(C5×D5)
unambiguous semidirect product(C2×D65)⋊(C5×C9)
unambiguous semidirect product(C2×C5×D65)⋊C9

Splittings

derivedC5×C13 ⋊ C22×C5×C9
HallC52×C13⋊C9 ⋊ C22
HallC2×C5×D65 ⋊ C9
HallC52×C13 ⋊ C22×C9
HallC13⋊C9 ⋊ C2×C5×D5
SylowC52 ⋊ C2×D13⋊C9
SylowC13 ⋊ C2×C5×C9×D5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C22×C5×C9
FrattiniC3C2×C5×C5⋊(D13⋊C3)
Fitting, socleC2×C3×C52×C13C2×C3
prime radicalC2×C3×C5×D65C3
cosocleC3×C5×C13C22×C3×C5
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C5

144 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 58 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

660 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 241);