Finite Group Databasebeta

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Cayley diagram

C11×SD16 #4334

order176
nilpotency class3
isoclinismisoclinic class of D8
automorphismAut(G) = C22×C5×D4 (order 160) · Inn(G) = D4 · Out(G) = C22×C5
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×SD16

Subgroups

subgroupG/H
center, socleC2×C11D4
commutator, Frattini, cosocleC4C22×C11
prime radicalD4×C11C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C4×C11 ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 88

A minimal faithful permutation representation — 2 generators on 19 points:

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

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofSD16×D11, #66967, #66968, …
maximal subgroup ofSD16×D11, #66967, #66968, …
maximal normal subgroup ofSD16×D11, #66967, #66968, …
maximal quotient ofC11×#102, C11×#103, C11×#106, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 25);