Finite Group Databasebeta

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Cayley diagram

C11×M16 #4332

order176
nilpotency class2
isoclinismisoclinic class of D4
automorphismAut(G) = C22×C5×D4 (order 160) · Inn(G) = C22 · Out(G) = C23×C5
homologyAbelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×M16

Subgroups

subgroupG/H
centerC4×C11C22
commutatorC2C2×C4×C11
Frattini, cosocleC4C22×C11
socleC2×C11C2×C4
prime radicalC22×C11C4
LCSG ▷ C2 ▷ C1
UCSC1 ◁ 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);(13,17)(15,19)

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of#66886, #66887, #66888, …
maximal subgroup of#66886, #66887, #66888, …
maximal normal subgroup of#66886, #66887, #66888, …
maximal quotient ofC11×#97, C11×C22⋊C8, C11×C4⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(176, 23);