Finite Group Databasebeta

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C2×C4×C8×C49 #72182884

order3136
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 86016
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C4×C8×C49
multiplicative(ℤ/6304)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4×C7C23×C7
socle, prime radicalC23×C7C2×C4×C7
LCSG ▷ C1
UCSC1 ◁ G

243 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 ofC2×C4×C16×C49, C2×C82×C49, C42×C8×C49, …
maximal normal subgroup ofC2×C4×C16×C49, C2×C82×C49, C42×C8×C49, …
maximal quotient ofC2×C4×C16×C49, C2×C82×C49, C42×C8×C49, …
automorphism group ofC32×C197
outer automorphism group ofC32×C197

GAP

Past the SmallGroups library coverage — no SmallGroups id.