Finite Group Databasebeta

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C2×C3×C4×C13×C32 #72188641

order9984
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 196608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C4×C13×C32
multiplicative(ℤ/15423)ˣ, (ℤ/18735)ˣ, (ℤ/19984)ˣ, (ℤ/20096)ˣ, (ℤ/20564)ˣ, (ℤ/21632)ˣ, (ℤ/24980)ˣ, (ℤ/30846)ˣ, (ℤ/37470)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C16C23×C3×C13
socle, prime radicalC23×C3×C13C2×C16
LCSG ▷ C1
UCSC1 ◁ G

540 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9984 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C13×C64, C2×C3×C8×C13×C32, C3×C42×C13×C32, …
maximal normal subgroup ofC2×C3×C4×C13×C64, C2×C3×C8×C13×C32, C3×C42×C13×C32, …
maximal quotient ofC2×C3×C4×C13×C64, C2×C3×C8×C13×C32, C3×C42×C13×C32, …
automorphism group ofC128×C169
outer automorphism group ofC128×C169

GAP

Past the SmallGroups library coverage — no SmallGroups id.