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C4×C5×C7×C83 #26042495

order11620
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3936
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC11620
abelianC4×C5×C7×C83
multiplicative(ℤ/11621)ˣ, (ℤ/23242)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C2×C5×C7×C83
socle, prime radicalC2×C5×C7×C83C2
LCSG ▷ C1
UCSC1 ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11620 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic11620, D23240
Fitting subgroup ofC4×C5×ΓL(1,𝔽8)×C83
maximal subgroup ofC3×C4×C5×C7×C83, C4×C5×ΓL(1,𝔽8)×C83, C5×C7×Dic3×C83, …
maximal normal subgroup ofC3×C4×C5×C7×C83, C4×C5×ΓL(1,𝔽8)×C83, C5×C7×C8×C83, …
maximal quotient ofC3×C4×C5×C7×C83, C5×C7×Dic3×C83, C5×C7×C8×C83, …
automorphism group ofC11621
outer automorphism group ofC11621

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11620, 1);