Finite Group Databasebeta

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C2×C4×C52×C43 #72187451

order8600
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 161280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C5

Aliases

abelianC2×C4×C52×C43
multiplicative(ℤ/10775)ˣ, (ℤ/21550)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C52×C43
socle, prime radicalC22×C52×C43C2
LCSG ▷ C1
UCSC1 ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C52×C8×C43, C42×C52×C43, C22×C4×C52×C43, …
maximal normal subgroup ofC2×C52×C8×C43, C42×C52×C43, C22×C4×C52×C43, …
maximal quotient ofC2×C52×C8×C43, C42×C52×C43, C22×C4×C52×C43, …
automorphism group ofC25×C431
outer automorphism group ofC25×C431

GAP

Past the SmallGroups library coverage — no SmallGroups id.