Finite Group Databasebeta

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C22×C3×C8×C121 #72190053

order11616
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 84480
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C8×C121
multiplicative(ℤ/23264)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C11C23×C3×C11
socle, prime radicalC23×C3×C11C4×C11
LCSG ▷ C1
UCSC1 ◁ G

228 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C16×C121, C2×C3×C4×C8×C121, C23×C3×C8×C121
maximal normal subgroup ofC22×C3×C16×C121, C2×C3×C4×C8×C121, C23×C3×C8×C121
maximal quotient ofC22×C3×C16×C121, C2×C3×C4×C8×C121, C23×C3×C8×C121

GAP

Past the SmallGroups library coverage — no SmallGroups id.