Finite Group Databasebeta

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C3×C4×C27×C32 #72188982

order10368
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 165888
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C4

Aliases

abelianC3×C4×C27×C32
multiplicative(ℤ/10573)ˣ, (ℤ/21146)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C9×C16C22×C32
socle, prime radicalC22×C32C2×C9×C16
LCSG ▷ C1
UCSC1 ◁ G

504 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C27×C64, C3×C8×C27×C32, C2×C3×C4×C27×C32, …
maximal normal subgroup ofC3×C4×C27×C64, C3×C8×C27×C32, C2×C3×C4×C27×C32, …
maximal quotient ofC3×C4×C27×C64, C3×C8×C27×C32, C2×C3×C4×C27×C32, …
automorphism group ofC97×C109
outer automorphism group ofC97×C109

GAP

Past the SmallGroups library coverage — no SmallGroups id.