Finite Group Databasebeta

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C2×C4×C7×C8×C17 #72186557

order7616
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 196608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C4×C7×C8×C17
multiplicative(ℤ/11919)ˣ, (ℤ/14295)ˣ, (ℤ/15248)ˣ, (ℤ/15892)ˣ, (ℤ/19060)ˣ, (ℤ/23838)ˣ, (ℤ/28590)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C23×C7×C17
socle, prime radicalC23×C7×C17C2×C4
LCSG ▷ C1
UCSC1 ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C7×C16×C17, C2×C7×C82×C17, C42×C7×C8×C17, …
maximal normal subgroup ofC2×C4×C7×C16×C17, C2×C7×C82×C17, C42×C7×C8×C17, …
maximal quotient ofC2×C4×C7×C16×C17, C2×C7×C82×C17, C42×C7×C8×C17, …
automorphism group ofC3×C29×C137
outer automorphism group ofC3×C29×C137

GAP

Past the SmallGroups library coverage — no SmallGroups id.