Finite Group Databasebeta

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C2×C32×C43×C13 #72193045

order14976
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3170893824
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3×C43

Aliases

abelianC2×C32×C43×C13
multiplicative(ℤ/24115)ˣ, (ℤ/30615)ˣ, (ℤ/31005)ˣ, (ℤ/32656)ˣ, (ℤ/40820)ˣ, (ℤ/48230)ˣ, (ℤ/61230)ˣ, (ℤ/62010)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23C24×C32×C13
socle, prime radicalC24×C32×C13C23
LCSG ▷ C1
UCSC1 ◁ G

7632 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14976 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C42×C8×C13, C32×C44×C13, C22×C32×C43×C13
maximal normal subgroup ofC2×C32×C42×C8×C13, C32×C44×C13, C22×C32×C43×C13
maximal quotient ofC2×C32×C42×C8×C13, C32×C44×C13, C22×C32×C43×C13
automorphism group ofC13×C16×C157
outer automorphism group ofC13×C16×C157

GAP

Past the SmallGroups library coverage — no SmallGroups id.