Finite Group Databasebeta

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C2×C4×C16×C49 #72185437

order6272
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 172032
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C4×C16×C49
multiplicative(ℤ/10047)ˣ, (ℤ/12608)ˣ, (ℤ/13396)ˣ, (ℤ/20094)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C7×C8C23×C7
socle, prime radicalC23×C7C2×C7×C8
LCSG ▷ C1
UCSC1 ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6272 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C32×C49, C2×C8×C16×C49, C42×C16×C49, …
maximal normal subgroup ofC2×C4×C32×C49, C2×C8×C16×C49, C42×C16×C49, …
maximal quotient ofC2×C4×C32×C49, C2×C8×C16×C49, C42×C16×C49, …
automorphism group ofC3×C17×C197
outer automorphism group ofC3×C17×C197

GAP

Past the SmallGroups library coverage — no SmallGroups id.