Finite Group Databasebeta

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C2×C4×C7×C179 #72188696

order10024
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8544
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C7×C179
multiplicative(ℤ/10411)ˣ, (ℤ/20822)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C7×C179
socle, prime radicalC22×C7×C179C2
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10024 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC42×C7×C179, C2×C7×C8×C179, C22×C4×C7×C179, …
maximal normal subgroup ofC42×C7×C179, C2×C7×C8×C179, C22×C4×C7×C179, …
maximal quotient ofC42×C7×C179, C2×C7×C8×C179, C22×C4×C7×C179, …
automorphism group ofC29×C359
outer automorphism group ofC29×C359

GAP

Past the SmallGroups library coverage — no SmallGroups id.