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C892 #21463693

order7921
nilpotency class1
isoclinismisoclinic class of C1
automorphism?
homologyAbelianization (H1) = G · Schur multiplier (H2) = C89

Aliases

abelianC892

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G
LECSG ▷ C1

92 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7921 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofC89⋊D89, C892⋊C3, #44540036, …
Fitting subgroup ofC89×D89, C89⋊D89, C892⋊C3, …
socle ofC89×D89, C89⋊D89, C892⋊C3, …
maximal subgroup ofC89×D89, C89⋊D89, C2×C892, …
maximal normal subgroup ofC89×D89, C89⋊D89, C2×C892, …
maximal quotient ofC2×C892, C3×C892

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7921, 2);