Finite Group Databasebeta

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C52×C7×C82 #72189684

order11200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4423680
homologyAbelianization (H1) = G · Schur multiplier (H2) = C5×C8

Aliases

abelianC52×C7×C82
multiplicative(ℤ/11521)ˣ, (ℤ/23042)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC42C22×C52×C7
socle, prime radicalC22×C52×C7C42
LCSG ▷ C1
UCSC1 ◁ G

592 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC52×C7×C8×C16, C2×C52×C7×C82
maximal normal subgroup ofC52×C7×C8×C16, C2×C52×C7×C82
maximal quotient ofC52×C7×C8×C16, C2×C52×C7×C82
automorphism group ofC41×C281
outer automorphism group ofC41×C281

GAP

Past the SmallGroups library coverage — no SmallGroups id.