Finite Group Databasebeta

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C2×C3×C8×C11×C23 #72190508

order12144
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7040
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C8×C11×C23
multiplicative(ℤ/12371)ˣ, (ℤ/18219)ˣ, (ℤ/24292)ˣ, (ℤ/24742)ˣ, (ℤ/36438)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C3×C11×C23
socle, prime radicalC22×C3×C11×C23C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12144 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C11×C16×C23, C3×C4×C8×C11×C23, C22×C3×C8×C11×C23
maximal normal subgroup ofC2×C3×C11×C16×C23, C3×C4×C8×C11×C23, C22×C3×C8×C11×C23
maximal quotient ofC2×C3×C11×C16×C23, C3×C4×C8×C11×C23, C22×C3×C8×C11×C23
automorphism group ofC89×C139
outer automorphism group ofC89×C139

GAP

Past the SmallGroups library coverage — no SmallGroups id.