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Cayley diagram

C42×#41 #33993

order256
nilpotency class2
isoclinismisoclinic class of D4
automorphismAut(G) order 4718592
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC42×#41

Subgroups

subgroupG/H
centerC43C22
commutatorC2C23×C42
Frattini, socle, cosocleC23C25
prime radicalC22×#41C22
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C43 ◁ G
LECSG ▷ C23 ▷ C1

2043 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 128

A minimal faithful permutation representation — 5 generators on 16 points:

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of#11709745, C42×#41⋊C3, #41×C42⋊C3
maximal subgroup of#105632, #105950, #180896, …
maximal normal subgroup of#105632, #105950, #180896, …
maximal quotient ofC42×#117, C43×D4, C43×Q8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 26981);