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Cayley diagram

C2×C43 #2265

order128
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5505024
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C43

Aliases

abelianC2×C43

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23C24
socle, prime radicalC24C23
LCSG ▷ C1
UCSC1 ◁ G
LECSG ▷ C23 ▷ C1

636 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 14
transitive degreeμt(G) = 128

A minimal faithful permutation representation — 4 generators on 14 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

center ofC4×#1273, C2×C4×#322, C2×#8131, …
derived subgroup of#72227994
Frattini subgroup of#92806, #92809, #92810, …
Fitting subgroup ofC2×C4×C42⋊C3, C2×#67995, #11710976, …
maximal subgroup ofC2×#1276, #7867, C4×#336, …
maximal normal subgroup ofC2×#1276, #7867, C4×#336, …
maximal quotient ofC44, C2×C4×#95, C4×#376, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 997);