Finite Group Databasebeta

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C3×C4×C8×C67 #72185589

order6432
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 16896
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC3×C4×C8×C67
multiplicative(ℤ/8045)ˣ, (ℤ/16090)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C22×C3×C67
socle, prime radicalC22×C3×C67C2×C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6432 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C16×C67, C3×C82×C67, C2×C3×C4×C8×C67, …
maximal normal subgroup ofC3×C4×C16×C67, C3×C82×C67, C2×C3×C4×C8×C67, …
maximal quotient ofC3×C4×C16×C67, C3×C82×C67, C2×C3×C4×C8×C67, …
automorphism group ofC5×C1609
outer automorphism group ofC5×C1609

GAP

Past the SmallGroups library coverage — no SmallGroups id.