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#737×C83 #20269594

order6723
nilpotency class2
isoclinismisoclinic class of H(3,𝔽3)
automorphism?
homologyAbelianization (H1) = C33×C83 · Schur multiplier (H2) = C32

Aliases

direct product#737×C83

Subgroups

subgroupG/H
centerC9×C83C32
commutator, FrattiniC3C33×C83
socleC3×C83C33
LCSG ▷ C3 ▷ C1
UCSC1 ◁ C9×C83 ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2739 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC83×#6872, C83×#6873, C83×#6903, …
maximal normal subgroup ofC83×#6872, C83×#6873, C83×#6903, …
maximal quotient ofC83×#6887, C9×H(3,𝔽3)×C83, C9×3−1+2×C83, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6723, 14);