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Cayley diagram

C8×#95 #10695

order256
nilpotency class2
isoclinismisoclinic class of D4
automorphismAut(G) order 196608
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×#95

Subgroups

subgroupG/H
centerC23×C8C22
commutatorC2C42×C8
Frattini, cosocleC23×C4C23
socle, prime radicalC24C22×C4
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C23×C8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

587 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 256

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofC8×#95⋊C3
maximal subgroup of#93410, C8×#327, C8×#328, …
maximal normal subgroup of#93410, C8×#327, C8×#328, …
maximal quotient ofC8×H(3,ℤ/4), C8×#338, C8×#340, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 3683);