Finite Group Databasebeta

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C2×C42×C5×C53 #72187357

order8480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 319488
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C42×C5×C53
multiplicative(ℤ/15915)ˣ, (ℤ/16976)ˣ, (ℤ/21220)ˣ, (ℤ/31830)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C5×C53
socle, prime radicalC23×C5×C53C22
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C5×C8×C53, C43×C5×C53, C22×C42×C5×C53, …
maximal normal subgroup ofC2×C4×C5×C8×C53, C43×C5×C53, C22×C42×C5×C53, …
maximal quotient ofC2×C4×C5×C8×C53, C43×C5×C53, C22×C42×C5×C53, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.