Finite Group Databasebeta

← Prev (#13183322) Next (#13183324) →

C23×C4×C11⋊C5 #13183323

order1760
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26

Aliases

direct productC23×C4×C11⋊C5
unambiguous semidirect product(C23×C4×C11)⋊C5

Splittings

Fitting, HallC23×C4×C11 ⋊ C5
derived, SylowC11 ⋊ C23×C4×C5

Subgroups

subgroupG/H
center, hypercenterC23×C4C11⋊C5
commutator, hypocenterC11C23×C4×C5
FrattiniC2C24×C11⋊C5
FittingC23×C4×C11C5
socleC24×C11C2×C5
prime radicalC24×C11⋊C5C2
cosocleC2×C11C24×C5
LCSG ▷ C11
UCSC1 ◁ C23×C4

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 352

A minimal faithful permutation representation — 4 generators on 21 points:

(1,2)(12,13,15,18,17)(14,16,20,21,19);(3,4)(11,12,14,17,13,15,19,21,16,18,20);(5,6);(7,8,9,10)

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×#525, C23×C4×AGL(1,𝔽11), #72248826, …
maximal normal subgroup ofC11⋊C5×#525, C23×C4×AGL(1,𝔽11), #72248826, …
maximal quotient ofC22×C22⋊C4×C11⋊C5, C11⋊C5×#518, C4×#41×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1132);