Finite Group Databasebeta

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C2×C11⋊C5×C169 #32915754

order18590
automorphism?
homologyAbelianization (H1) = C2×C5×C169 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11⋊C5×C169
unambiguous semidirect product(C2×C11)⋊(C5×C169)
unambiguous semidirect product(C2×C11×C169)⋊C5

Splittings

Fitting, HallC2×C11×C169 ⋊ C5
derived, SylowC11 ⋊ C2×C5×C169
HallC11×C169 ⋊ C2×C5
HallC2×C11 ⋊ C5×C169

Subgroups

subgroupG/H
center, hypercenterC2×C169C11⋊C5
commutator, hypocenterC11C2×C5×C169
FrattiniC13C2×C13×C11⋊C5
FittingC2×C11×C169C5
socleC2×C11×C13C5×C13
prime radicalC2×C13×C11⋊C5C13
cosocleC11×C13C2×C5×C13
LCSG ▷ C11
UCSC1 ◁ C2×C169

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3718

Conjugacy classes & character table

2366 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11⋊C5×Dic169, C169×Dic11⋊C5, (C11⋊C5)⋊Dic169, …
maximal normal subgroup ofC11⋊C5×Dic169, C169×Dic11⋊C5, (C11⋊C5)⋊Dic169, …
maximal quotient ofC4×C11⋊C5×C169, C22×C11⋊C5×C169

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18590, 5);