Finite Group Databasebeta

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C3×C4×C72×C16 #72188170

order9408
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1032192
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4×C7

Aliases

abelianC3×C4×C72×C16
multiplicative(ℤ/9773)ˣ, (ℤ/19546)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C22×C3×C72
socle, prime radicalC22×C3×C72C2×C8
LCSG ▷ C1
UCSC1 ◁ G

580 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9408 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C72×C32, C3×C72×C8×C16, C2×C3×C4×C72×C16, …
maximal normal subgroup ofC3×C4×C72×C32, C3×C72×C8×C16, C2×C3×C4×C72×C16, …
maximal quotient ofC3×C4×C72×C32, C3×C72×C8×C16, C2×C3×C4×C72×C16, …
automorphism group ofC29×C337
outer automorphism group ofC29×C337

GAP

Past the SmallGroups library coverage — no SmallGroups id.