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C4×C5×C23⋊C11 #19099415

order5060
isoclinismisoclinic class of C23⋊C11
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C23⋊C11
unambiguous semidirect product(C4×C23)⋊(C5×C11)
unambiguous semidirect product(C4×C5×C23)⋊C11

Splittings

Fitting, HallC4×C5×C23 ⋊ C11
derived, SylowC23 ⋊ C4×C5×C11
HallC5×C23 ⋊ C4×C11
HallC4×C23 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC4×C5C23⋊C11
commutator, hypocenterC23C4×C5×C11
FrattiniC2C2×C5×C23⋊C11
FittingC4×C5×C23C11
socleC2×C5×C23C2×C11
LCSG ▷ C23
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

260 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×C5×C23⋊C11, C5×Dic3×C23⋊C11, C4×C25×C23⋊C11, …
maximal normal subgroup ofC3×C4×C5×C23⋊C11, C4×C25×C23⋊C11, C4×C52×C23⋊C11, …
maximal quotient ofC3×C4×C5×C23⋊C11, C5×Dic3×C23⋊C11, C4×C25×C23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5060, 2);