Finite Group Databasebeta

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C22×C3×C4×C9×C32 #72192013

order13824
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 84934656
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4

Aliases

abelianC22×C3×C4×C9×C32
multiplicative(ℤ/27645)ˣ, (ℤ/28712)ˣ, (ℤ/29488)ˣ, (ℤ/31616)ˣ, (ℤ/33152)ˣ, (ℤ/36860)ˣ, (ℤ/41904)ˣ, (ℤ/42624)ˣ, (ℤ/43068)ˣ, (ℤ/44928)ˣ, (ℤ/52380)ˣ, (ℤ/55290)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C16C24×C32
socle, prime radicalC24×C32C2×C3×C16
LCSG ▷ C1
UCSC1 ◁ G

6420 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C9×C64, C22×C3×C8×C9×C32, C2×C3×C42×C9×C32, …
maximal normal subgroup ofC22×C3×C4×C9×C64, C22×C3×C8×C9×C32, C2×C3×C42×C9×C32, …
maximal quotient ofC22×C3×C4×C9×C64, C22×C3×C8×C9×C32, C2×C3×C42×C9×C32, …
automorphism group ofC8×C37×C97, C16×C19×C97, C13×C19×C128
outer automorphism group ofC8×C37×C97, C16×C19×C97, C13×C19×C128

GAP

Past the SmallGroups library coverage — no SmallGroups id.