Finite Group Databasebeta

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C32×C4×C5×C16 #72182663

order2880
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 49152
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C4

Aliases

abelianC32×C4×C5×C16
multiplicative(ℤ/3133)ˣ, (ℤ/6266)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C22×C32×C5
socle, prime radicalC22×C32×C5C2×C8
LCSG ▷ C1
UCSC1 ◁ G

348 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2880 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C4×C5×C32, C32×C5×C8×C16, C2×C32×C4×C5×C16, …
maximal normal subgroup ofC32×C4×C5×C32, C32×C5×C8×C16, C2×C32×C4×C5×C16, …
maximal quotient ofC32×C4×C5×C32, C32×C5×C8×C16, C2×C32×C4×C5×C16, …
automorphism group ofC13×C241, C2×C13×C241
outer automorphism group ofC13×C241, C2×C13×C241

GAP

Past the SmallGroups library coverage — no SmallGroups id.