Finite Group Databasebeta

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C4×C49×C64 #72190884

order12544
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 43008
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C49×C64
multiplicative(ℤ/15685)ˣ, (ℤ/31370)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C7×C32C22×C7
socle, prime radicalC22×C7C2×C7×C32
LCSG ▷ C1
UCSC1 ◁ G

129 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12544 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C49×C128, C8×C49×C64, C2×C4×C49×C64
maximal normal subgroup ofC4×C49×C128, C8×C49×C64, C2×C4×C49×C64
maximal quotient ofC4×C49×C128, C8×C49×C64, C2×C4×C49×C64
automorphism group ofC5×C3137
outer automorphism group ofC5×C3137

GAP

Past the SmallGroups library coverage — no SmallGroups id.