Finite Group Databasebeta

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#509×C97 #20260376

order6208
nilpotency class4
isoclinismisoclinic class of #509
automorphism?
homologyAbelianization (H1) = C23×C97 · Schur multiplier (H2) = C22

Aliases

direct product#509×C97

Subgroups

subgroupG/H
center, socleC2×C97C2×D8
commutator, Frattini, cosocleC8C23×C97
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C97 ◁ C2×C4×C97 ◁ C2×C8×C97 ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1552 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC97×AGL(1,ℤ/16), C97×#2190, C97×#2192, …
maximal normal subgroup ofC97×AGL(1,ℤ/16), C97×#2190, C97×#2192, …
maximal quotient ofC97×#2139, C97×#2140, C97×#2159, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 190);