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C2×C43×C64 #19130244

order5504
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5376
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C43×C64
multiplicative(ℤ/8259)ˣ, (ℤ/11012)ˣ, (ℤ/16518)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
FrattiniC32C22×C43
socleC22×C43C32
LCSG ▷ C1
UCSC1 ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5504 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C43×C64, C43×#7510, C43×C22⋊C64, …
maximal normal subgroup ofC4×C43×C64, C43×#7510, C43×C22⋊C64, …
maximal quotient ofC4×C43×C64, C43×C22⋊C64, C43×C4⋊C64, …
automorphism group ofC3×C2753, C4×C2753
outer automorphism group ofC3×C2753, C4×C2753

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5504, 159);