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C2×C3×C8×C11×C31 #72194286

order16368
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C8×C11×C31
multiplicative(ℤ/19103)ˣ, (ℤ/24561)ˣ, (ℤ/38206)ˣ, (ℤ/49122)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C3×C11×C31
socle, prime radicalC22×C3×C11×C31C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C11×C16×C31, C3×C4×C8×C11×C31, C22×C3×C8×C11×C31
maximal normal subgroup ofC2×C3×C11×C16×C31, C3×C4×C8×C11×C31, C22×C3×C8×C11×C31
maximal quotient ofC2×C3×C11×C16×C31, C3×C4×C8×C11×C31, C22×C3×C8×C11×C31
automorphism group ofC7×C2729
outer automorphism group ofC7×C2729

GAP

Past the SmallGroups library coverage — no SmallGroups id.