Finite Group Databasebeta

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C2×C4×C5×C11×C29 #72191076

order12760
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8960
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C5×C11×C29
multiplicative(ℤ/14047)ˣ, (ℤ/15955)ˣ, (ℤ/28094)ˣ, (ℤ/31910)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C5×C11×C29
socle, prime radicalC22×C5×C11×C29C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12760 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC42×C5×C11×C29, C2×C5×C8×C11×C29, C22×C4×C5×C11×C29
maximal normal subgroup ofC42×C5×C11×C29, C2×C5×C8×C11×C29, C22×C4×C5×C11×C29
maximal quotient ofC42×C5×C11×C29, C2×C5×C8×C11×C29, C22×C4×C5×C11×C29
automorphism group ofC11×C1277, C5×C3191
outer automorphism group ofC11×C1277, C5×C3191

GAP

Past the SmallGroups library coverage — no SmallGroups id.