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C5×C13×C23⋊C11 #30656182

order16445
isoclinismisoclinic class of C23⋊C11
automorphism?
homologyAbelianization (H1) = C5×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×C23⋊C11
unambiguous semidirect productC23⋊(C5×C11×C13)
unambiguous semidirect product(C5×C23)⋊(C11×C13)
unambiguous semidirect product(C13×C23)⋊(C5×C11)
unambiguous semidirect product(C5×C13×C23)⋊C11

Splittings

Fitting, socle, HallC5×C13×C23 ⋊ C11
derived, SylowC23 ⋊ C5×C11×C13
HallC13×C23 ⋊ C5×C11
HallC5×C23 ⋊ C11×C13

Subgroups

subgroupG/H
center, hypercenterC5×C13C23⋊C11
commutator, cosocle, hypocenterC23C5×C11×C13
FrattiniC1G
Fitting, socleC5×C13×C23C11
LCSG ▷ C23
UCSC1 ◁ C5×C13

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1495

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C5×C13×C23⋊C11, C5×C13×AGL(1,𝔽23), C5×D13×C23⋊C11, …
maximal normal subgroup ofC2×C5×C13×C23⋊C11, C5×C13×AGL(1,𝔽23), C5×D13×C23⋊C11, …
maximal quotient ofC2×C5×C13×C23⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16445, 2);