Finite Group Databasebeta

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C4×C16×C49 #72182878

order3136
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10752
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C16×C49
multiplicative(ℤ/3349)ˣ, (ℤ/6698)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C7×C8C22×C7
socle, prime radicalC22×C7C2×C7×C8
LCSG ▷ C1
UCSC1 ◁ G

87 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3136 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C32×C49, C8×C16×C49, C2×C4×C16×C49, …
maximal normal subgroup ofC4×C32×C49, C8×C16×C49, C2×C4×C16×C49, …
maximal quotient ofC4×C32×C49, C8×C16×C49, C2×C4×C16×C49, …
automorphism group ofC17×C197, C2×C17×C197
outer automorphism group ofC17×C197, C2×C17×C197

GAP

Past the SmallGroups library coverage — no SmallGroups id.