Finite Group Databasebeta

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C32×C5×C8×C32 #72189943

order11520
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 786432
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C8

Aliases

abelianC32×C5×C8×C32

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C16C22×C32×C5
socle, prime radicalC22×C32×C5C4×C16
LCSG ▷ C1
UCSC1 ◁ G

804 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×C8×C64, C32×C5×C16×C32, C2×C32×C5×C8×C32
maximal normal subgroup ofC32×C5×C8×C64, C32×C5×C16×C32, C2×C32×C5×C8×C32
maximal quotient ofC32×C5×C8×C64, C32×C5×C16×C32, C2×C32×C5×C8×C32

GAP

Past the SmallGroups library coverage — no SmallGroups id.