Finite Group Databasebeta

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C24×C5×C173 #72192079

order13840
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 13870080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C5×C173
multiplicative(ℤ/30536)ˣ, (ℤ/45804)ˣ

Subgroups

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

268 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC25×C5×C173, C23×C4×C5×C173
maximal normal subgroup ofC25×C5×C173, C23×C4×C5×C173
maximal quotient ofC25×C5×C173, C23×C4×C5×C173
automorphism group ofC8×C11×C347
outer automorphism group ofC8×C11×C347

GAP

Past the SmallGroups library coverage — no SmallGroups id.