Finite Group Databasebeta

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C22×C4×C7×C9×C11 #72189604

order11088
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 69120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C7×C9×C11
multiplicative(ℤ/12673)ˣ, (ℤ/14605)ˣ, (ℤ/17313)ˣ, (ℤ/18009)ˣ, (ℤ/23084)ˣ, (ℤ/25346)ˣ, (ℤ/29210)ˣ, (ℤ/34626)ˣ, (ℤ/36018)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C23×C3×C7×C11
socle, prime radicalC23×C3×C7×C11C2×C3
LCSG ▷ C1
UCSC1 ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11088 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C7×C8×C9×C11, C2×C42×C7×C9×C11, C23×C4×C7×C9×C11
maximal normal subgroup ofC22×C7×C8×C9×C11, C2×C42×C7×C9×C11, C23×C4×C7×C9×C11
maximal quotient ofC22×C7×C8×C9×C11, C2×C42×C7×C9×C11, C23×C4×C7×C9×C11
automorphism group ofC19×C23×C29, C5×C23×C127, C23×C27×C29
outer automorphism group ofC19×C23×C29, C5×C23×C127, C23×C27×C29

GAP

Past the SmallGroups library coverage — no SmallGroups id.