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C2×C4×C5×C9×C31 #72189656

order11160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C5×C9×C31
multiplicative(ℤ/11507)ˣ, (ℤ/12287)ˣ, (ℤ/13955)ˣ, (ℤ/16743)ˣ, (ℤ/22324)ˣ, (ℤ/23014)ˣ, (ℤ/24574)ˣ, (ℤ/27910)ˣ, (ℤ/33486)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C22×C3×C5×C31
socle, prime radicalC22×C3×C5×C31C2×C3
LCSG ▷ C1
UCSC1 ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C8×C9×C31, C42×C5×C9×C31, C22×C4×C5×C9×C31
maximal normal subgroup ofC2×C5×C8×C9×C31, C42×C5×C9×C31, C22×C4×C5×C9×C31
maximal quotient ofC2×C5×C8×C9×C31, C42×C5×C9×C31, C22×C4×C5×C9×C31
automorphism group ofC37×C311, C11×C1117, C5×C2791
outer automorphism group ofC37×C311, C11×C1117, C5×C2791

GAP

Past the SmallGroups library coverage — no SmallGroups id.