Finite Group Databasebeta

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#509×C193 #27134900

order12352
nilpotency class4
isoclinismisoclinic class of #509
automorphism?
homologyAbelianization (H1) = C23×C193 · Schur multiplier (H2) = C22

Aliases

direct product#509×C193

Subgroups

subgroupG/H
center, socleC2×C193C2×D8
commutator, Frattini, cosocleC8C23×C193
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C193 ◁ C2×C4×C193 ◁ C2×C8×C193 ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3088 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,ℤ/16)×C193, #2190×C193, #2192×C193, …
maximal normal subgroup ofAGL(1,ℤ/16)×C193, #2190×C193, #2192×C193, …
maximal quotient of#2139×C193, #2140×C193, #2159×C193, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 190);