Finite Group Databasebeta

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C3×C4×C8×C47 #72183996

order4512
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 11776
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC3×C4×C8×C47
multiplicative(ℤ/5645)ˣ, (ℤ/11290)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C22×C3×C47
socle, prime radicalC22×C3×C47C2×C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C16×C47, C3×C82×C47, C2×C3×C4×C8×C47, …
maximal normal subgroup ofC3×C4×C16×C47, C3×C82×C47, C2×C3×C4×C8×C47, …
maximal quotient ofC3×C4×C16×C47, C3×C82×C47, C2×C3×C4×C8×C47, …
automorphism group ofC5×C1129
outer automorphism group ofC5×C1129

GAP

Past the SmallGroups library coverage — no SmallGroups id.