Finite Group Databasebeta

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C2×C3×C5×C256 #72186589

order7680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4096
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C5×C256
multiplicative(ℤ/7967)ˣ, (ℤ/8459)ˣ, (ℤ/15934)ˣ, (ℤ/16918)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC128C22×C3×C5
socle, prime radicalC22×C3×C5C128
LCSG ▷ C1
UCSC1 ◁ G

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C512, C3×C4×C5×C256, C22×C3×C5×C256, …
maximal normal subgroup ofC2×C3×C5×C512, C3×C4×C5×C256, C22×C3×C5×C256, …
maximal quotient ofC2×C3×C5×C512, C3×C4×C5×C256, C22×C3×C5×C256, …
automorphism group ofC31×C257, C11×C769
outer automorphism group ofC31×C257, C11×C769

GAP

Past the SmallGroups library coverage — no SmallGroups id.