Finite Group Databasebeta

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C22×C8×C11×C41 #72192603

order14432
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 153600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C8×C11×C41
multiplicative(ℤ/22161)ˣ, (ℤ/29548)ˣ, (ℤ/44322)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C11×C41
socle, prime radicalC23×C11×C41C4
LCSG ▷ C1
UCSC1 ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14432 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C11×C16×C41, C2×C4×C8×C11×C41, C23×C8×C11×C41
maximal normal subgroup ofC22×C11×C16×C41, C2×C4×C8×C11×C41, C23×C8×C11×C41
maximal quotient ofC22×C11×C16×C41, C2×C4×C8×C11×C41, C23×C8×C11×C41

GAP

Past the SmallGroups library coverage — no SmallGroups id.