Finite Group Databasebeta

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C2×C4×C7×C11×C17 #72189092

order10472
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7680
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C7×C11×C17
multiplicative(ℤ/15711)ˣ, (ℤ/20948)ˣ, (ℤ/31422)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C7×C11×C17
socle, prime radicalC22×C7×C11×C17C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10472 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C8×C11×C17, C42×C7×C11×C17, C22×C4×C7×C11×C17, …
maximal normal subgroup ofC2×C7×C8×C11×C17, C42×C7×C11×C17, C22×C4×C7×C11×C17, …
maximal quotient ofC2×C7×C8×C11×C17, C42×C7×C11×C17, C22×C4×C7×C11×C17, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.