Finite Group Databasebeta

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C22×C42×C5×C11 #72183179

order3520
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5898240
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C42×C5×C11
multiplicative(ℤ/9200)ˣ, (ℤ/9680)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C24×C5×C11
socle, prime radicalC24×C5×C11C22
LCSG ▷ C1
UCSC1 ◁ G

996 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C5×C8×C11, C2×C43×C5×C11, C23×C42×C5×C11, …
maximal normal subgroup ofC22×C4×C5×C8×C11, C2×C43×C5×C11, C23×C42×C5×C11, …
maximal quotient ofC22×C4×C5×C8×C11, C2×C43×C5×C11, C23×C42×C5×C11, …
automorphism group ofC16×C23×C25, C5×C16×C121
outer automorphism group ofC16×C23×C25, C5×C16×C121

GAP

Past the SmallGroups library coverage — no SmallGroups id.