Finite Group Databasebeta

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C2×C32×C42×C23 #72185753

order6624
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1622016
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4

Aliases

abelianC2×C32×C42×C23
multiplicative(ℤ/9035)ˣ, (ℤ/9695)ˣ, (ℤ/10803)ˣ, (ℤ/12465)ˣ, (ℤ/14404)ˣ, (ℤ/18070)ˣ, (ℤ/19390)ˣ, (ℤ/21606)ˣ, (ℤ/24930)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C32×C23
socle, prime radicalC23×C32×C23C22
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C4×C8×C23, C32×C43×C23, C22×C32×C42×C23, …
maximal normal subgroup ofC2×C32×C4×C8×C23, C32×C43×C23, C22×C32×C42×C23, …
maximal quotient ofC2×C32×C4×C8×C23, C32×C43×C23, C22×C32×C42×C23, …
automorphism group ofC5×C13×C139, C5×C7×C277, C3×C13×C277
outer automorphism group ofC5×C13×C139, C5×C7×C277, C3×C13×C277

GAP

Past the SmallGroups library coverage — no SmallGroups id.