Finite Group Databasebeta

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C42×C5×C8×C13 #72187243

order8320
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4718592
homologyAbelianization (H1) = G · Schur multiplier (H2) = C43

Aliases

abelianC42×C5×C8×C13
multiplicative(ℤ/10865)ˣ, (ℤ/21730)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C4C23×C5×C13
socle, prime radicalC23×C5×C13C22×C4
LCSG ▷ C1
UCSC1 ◁ G

816 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC42×C5×C13×C16, C4×C5×C82×C13, C2×C42×C5×C8×C13, …
maximal normal subgroup ofC42×C5×C13×C16, C4×C5×C82×C13, C2×C42×C5×C8×C13, …
maximal quotient ofC42×C5×C13×C16, C4×C5×C82×C13, C2×C42×C5×C8×C13, …
automorphism group ofC5×C41×C53
outer automorphism group ofC5×C41×C53

GAP

Past the SmallGroups library coverage — no SmallGroups id.