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C4×C23×C11⋊C5 #19099416

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

Aliases

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

Splittings

Fitting, HallC4×C11×C23 ⋊ C5
derived, SylowC11 ⋊ C4×C5×C23
HallC11×C23 ⋊ C4×C5
HallC4×C11 ⋊ C5×C23

Subgroups

subgroupG/H
center, hypercenterC4×C23C11⋊C5
commutator, hypocenterC11C4×C5×C23
FrattiniC2C2×C23×C11⋊C5
FittingC4×C11×C23C5
socleC2×C11×C23C2×C5
LCSG ▷ C11
UCSC1 ◁ C4×C23

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

644 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×C23×C11⋊C5, Dic3×C23×C11⋊C5, Dic5×C23×C11⋊C5, …
maximal normal subgroup ofC3×C4×C23×C11⋊C5, C4×C5×C23×C11⋊C5, C4×C7×C23×C11⋊C5
maximal quotient ofC3×C4×C23×C11⋊C5, Dic3×C23×C11⋊C5, C4×C23×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5060, 3);