Finite Group Databasebeta

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#509×C103 #20267432

order6592
nilpotency class4
isoclinismisoclinic class of #509
automorphism?
homologyAbelianization (H1) = C23×C103 · Schur multiplier (H2) = C22

Aliases

direct product#509×C103

Subgroups

subgroupG/H
center, socleC2×C103C2×D8
commutator, Frattini, cosocleC8C23×C103
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C2×C4×C103 ◁ C2×C8×C103 ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1648 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC103×AGL(1,ℤ/16), C103×#2190, C103×#2192, …
maximal normal subgroup ofC103×AGL(1,ℤ/16), C103×#2190, C103×#2192, …
maximal quotient ofC103×#2139, C103×#2140, C103×#2159, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6592, 190);