Finite Group Databasebeta

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C23×C5×C179 #72186203

order7160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 119616
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C5×C179
multiplicative(ℤ/11847)ˣ, (ℤ/15796)ˣ, (ℤ/23694)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C5×C179, C24×C5×C179, C23×C3×C5×C179
maximal normal subgroup ofC22×C4×C5×C179, C24×C5×C179, C23×C3×C5×C179
maximal quotient ofC22×C4×C5×C179, C24×C5×C179, C23×C3×C5×C179
automorphism group ofC3×C11×C359
outer automorphism group ofC3×C11×C359

GAP

Past the SmallGroups library coverage — no SmallGroups id.