Finite Group Databasebeta

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C22×C8×C11×C17 #72185181

order5984
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 61440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C8×C11×C17
multiplicative(ℤ/9453)ˣ, (ℤ/12604)ˣ, (ℤ/18906)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C11×C17
socle, prime radicalC23×C11×C17C4
LCSG ▷ C1
UCSC1 ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5984 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C11×C16×C17, C2×C4×C8×C11×C17, C23×C8×C11×C17, …
maximal normal subgroup ofC22×C11×C16×C17, C2×C4×C8×C11×C17, C23×C8×C11×C17, …
maximal quotient ofC22×C11×C16×C17, C2×C4×C8×C11×C17, C23×C8×C11×C17, …
automorphism group ofC3×C23×C137
outer automorphism group ofC3×C23×C137

GAP

Past the SmallGroups library coverage — no SmallGroups id.