Finite Group Databasebeta

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C2×C3×C42×C11×C13 #72191932

order13728
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 368640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C42×C11×C13
multiplicative(ℤ/15847)ˣ, (ℤ/17755)ˣ, (ℤ/18055)ˣ, (ℤ/19435)ˣ, (ℤ/31694)ˣ, (ℤ/35510)ˣ, (ℤ/36110)ˣ, (ℤ/38870)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C3×C11×C13
socle, prime radicalC23×C3×C11×C13C22
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13728 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C8×C11×C13, C3×C43×C11×C13, C22×C3×C42×C11×C13
maximal normal subgroup ofC2×C3×C4×C8×C11×C13, C3×C43×C11×C13, C22×C3×C42×C11×C13
maximal quotient ofC2×C3×C4×C8×C11×C13, C3×C43×C11×C13, C22×C3×C42×C11×C13
automorphism group ofC5×C53×C67, C5×C23×C157
outer automorphism group ofC5×C53×C67, C5×C23×C157

GAP

Past the SmallGroups library coverage — no SmallGroups id.