Finite Group Databasebeta

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C4×C7×C256 #72186206

order7168
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 24576
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C7×C256
multiplicative(ℤ/7453)ˣ, (ℤ/14906)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C128C22×C7
socle, prime radicalC22×C7C2×C128
LCSG ▷ C1
UCSC1 ◁ G

114 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7168 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C7×C512, C7×C8×C256, C2×C4×C7×C256, …
maximal normal subgroup ofC4×C7×C512, C7×C8×C256, C2×C4×C7×C256, …
maximal quotient ofC4×C7×C512, C7×C8×C256, C2×C4×C7×C256, …
automorphism group ofC29×C257
outer automorphism group ofC29×C257

GAP

Past the SmallGroups library coverage — no SmallGroups id.