Finite Group Databasebeta

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C2×C4×C7×C128 #72186209

order7168
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 196608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C4×C7×C128
multiplicative(ℤ/14848)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C64C23×C7
socle, prime radicalC23×C7C2×C64
LCSG ▷ C1
UCSC1 ◁ G

378 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 ofC2×C4×C7×C256, C2×C7×C8×C128, C42×C7×C128, …
maximal normal subgroup ofC2×C4×C7×C256, C2×C7×C8×C128, C42×C7×C128, …
maximal quotient ofC2×C4×C7×C256, C2×C7×C8×C128, C42×C7×C128, …
automorphism group ofC29×C512
outer automorphism group ofC29×C512

GAP

Past the SmallGroups library coverage — no SmallGroups id.