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C9×D5×C112 #24926124

order10890
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C9×C112 · Schur multiplier (H2) = C11

Aliases

direct productC9×D5×C112
unambiguous semidirect productC5⋊(C2×C9×C112)

Splittings

Fitting, HallC5×C9×C112 ⋊ C2
derived, SylowC5 ⋊ C2×C9×C112
HallC5×C112 ⋊ C2×C9
HallC5×C9 ⋊ C2×C112

Subgroups

subgroupG/H
center, hypercenterC9×C112D5
commutator, hypocenterC5C2×C9×C112
FrattiniC3C3×D5×C112
FittingC5×C9×C112C2
socleC3×C5×C112C2×C3
prime radicalC3×D5×C112C3
cosocleC3×C5C2×C3×C112
LCSG ▷ C5
UCSC1 ◁ C9×C112

168 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4356 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C112×AGL(1,𝔽5), C9×C11×C11⋊AGL(1,𝔽5), C9×C11⋊(C11⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC9×C112×AGL(1,𝔽5), C9×C11×C11⋊AGL(1,𝔽5), C9×C11⋊(C11⋊AGL(1,𝔽5)), …
maximal quotient ofC9×C112×Dic5, C2×C9×D5×C112

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 73);