Finite Group Databasebeta

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C22×C43×C5×C11 #72192248

order14080
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 84557168640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C27×C43

Aliases

abelianC22×C43×C5×C11

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23C25×C5×C11
socle, prime radicalC25×C5×C11C23
LCSG ▷ C1
UCSC1 ◁ G

16188 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C42×C5×C8×C11, C2×C44×C5×C11, C23×C43×C5×C11
maximal normal subgroup ofC22×C42×C5×C8×C11, C2×C44×C5×C11, C23×C43×C5×C11
maximal quotient ofC22×C42×C5×C8×C11, C2×C44×C5×C11, C23×C43×C5×C11

GAP

Past the SmallGroups library coverage — no SmallGroups id.