Finite Group Databasebeta

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C22×C3×C42×C5×C8 #72186610

order7680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 19327352832
homologyAbelianization (H1) = G · Schur multiplier (H2) = C27×C43

Aliases

abelianC22×C3×C42×C5×C8
multiplicative(ℤ/21320)ˣ, (ℤ/22880)ˣ, (ℤ/22960)ˣ, (ℤ/25584)ˣ, (ℤ/29280)ˣ, (ℤ/29520)ˣ, (ℤ/31200)ˣ, (ℤ/31980)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C4C25×C3×C5
socle, prime radicalC25×C3×C5C22×C4
LCSG ▷ C1
UCSC1 ◁ G

26376 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C42×C5×C16, C22×C3×C4×C5×C82, C2×C3×C43×C5×C8, …
maximal normal subgroup ofC22×C3×C42×C5×C16, C22×C3×C4×C5×C82, C2×C3×C43×C5×C8, …
maximal quotient ofC22×C3×C42×C5×C16, C22×C3×C4×C5×C82, C2×C3×C43×C5×C8, …
automorphism group ofC5×C8×C13×C41, C5×C11×C13×C32, C5×C7×C16×C41, …
outer automorphism group ofC5×C8×C13×C41, C5×C11×C13×C32, C5×C7×C16×C41, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.