Finite Group Databasebeta

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C2×C7×C16×C43 #72188351

order9632
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8064
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C7×C16×C43
multiplicative(ℤ/14451)ˣ, (ℤ/19268)ˣ, (ℤ/28902)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C7×C43
socle, prime radicalC22×C7×C43C8
LCSG ▷ C1
UCSC1 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9632 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C32×C43, C4×C7×C16×C43, C22×C7×C16×C43, …
maximal normal subgroup ofC2×C7×C32×C43, C4×C7×C16×C43, C22×C7×C16×C43, …
maximal quotient ofC2×C7×C32×C43, C4×C7×C16×C43, C22×C7×C16×C43, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.