Finite Group Databasebeta

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C22×C4×C11×C47 #72187206

order8272
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 88320
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C11×C47
multiplicative(ℤ/16552)ˣ, (ℤ/24828)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C11×C47
socle, prime radicalC23×C11×C47C2
LCSG ▷ C1
UCSC1 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8272 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C42×C11×C47, C22×C8×C11×C47, C23×C4×C11×C47, …
maximal normal subgroup ofC2×C42×C11×C47, C22×C8×C11×C47, C23×C4×C11×C47, …
maximal quotient ofC2×C42×C11×C47, C22×C8×C11×C47, C23×C4×C11×C47, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.