Finite Group Databasebeta

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C2×C32×C4×C5×C31 #72189658

order11160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 46080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC2×C32×C4×C5×C31
multiplicative(ℤ/11563)ˣ, (ℤ/12493)ˣ, (ℤ/13027)ˣ, (ℤ/16749)ˣ, (ℤ/23126)ˣ, (ℤ/24986)ˣ, (ℤ/26054)ˣ, (ℤ/33498)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C32×C5×C31
socle, prime radicalC22×C32×C5×C31C2
LCSG ▷ C1
UCSC1 ◁ G

192 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×C32×C5×C8×C31, C32×C42×C5×C31, C22×C32×C4×C5×C31
maximal normal subgroup ofC2×C32×C5×C8×C31, C32×C42×C5×C31, C22×C32×C4×C5×C31
maximal quotient ofC2×C32×C5×C8×C31, C32×C42×C5×C31, C22×C32×C4×C5×C31
automorphism group ofC31×C373, C7×C1861
outer automorphism group ofC31×C373, C7×C1861

GAP

Past the SmallGroups library coverage — no SmallGroups id.