Finite Group Databasebeta

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#509×C101 #20264818

order6464
nilpotency class4
isoclinismisoclinic class of #509
automorphism?
homologyAbelianization (H1) = C23×C101 · Schur multiplier (H2) = C22

Aliases

direct product#509×C101

Subgroups

subgroupG/H
center, socleC2×C101C2×D8
commutator, Frattini, cosocleC8C23×C101
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C2×C4×C101 ◁ C2×C8×C101 ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC101×AGL(1,ℤ/16), C101×#2190, C101×#2192, …
maximal normal subgroup ofC101×AGL(1,ℤ/16), C101×#2190, C101×#2192, …
maximal quotient ofC101×#2139, C101×#2140, C101×#2159, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6464, 190);