Finite Group Databasebeta

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C22×C33×C4×C11 #72184207

order4752
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 21565440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C33

Aliases

abelianC22×C33×C4×C11
multiplicative(ℤ/6097)ˣ, (ℤ/7839)ˣ, (ℤ/12194)ˣ, (ℤ/15678)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C33×C11
socle, prime radicalC23×C33×C11C2
LCSG ▷ C1
UCSC1 ◁ G

1512 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4752 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C33×C8×C11, C2×C33×C42×C11, C23×C33×C4×C11, …
maximal normal subgroup ofC22×C33×C8×C11, C2×C33×C42×C11, C23×C33×C4×C11, …
maximal quotient ofC22×C33×C8×C11, C2×C33×C42×C11, C23×C33×C4×C11, …
automorphism group ofC7×C13×C67, C9×C13×C67
outer automorphism group ofC7×C13×C67, C9×C13×C67

GAP

Past the SmallGroups library coverage — no SmallGroups id.