Finite Group Databasebeta

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C2×C3×C5×C16×C29 #72192131

order13920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7168
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C5×C16×C29
multiplicative(ℤ/14219)ˣ, (ℤ/20883)ˣ, (ℤ/27844)ˣ, (ℤ/28438)ˣ, (ℤ/41766)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C3×C5×C29
socle, prime radicalC22×C3×C5×C29C8
LCSG ▷ C1
UCSC1 ◁ G

112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C29×C32, C3×C4×C5×C16×C29, C22×C3×C5×C16×C29
maximal normal subgroup ofC2×C3×C5×C29×C32, C3×C4×C5×C16×C29, C22×C3×C5×C16×C29
maximal quotient ofC2×C3×C5×C29×C32, C3×C4×C5×C16×C29, C22×C3×C5×C16×C29
automorphism group ofC59×C241
outer automorphism group ofC59×C241

GAP

Past the SmallGroups library coverage — no SmallGroups id.