Finite Group Databasebeta

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#509×C157 #23756914

order10048
nilpotency class4
isoclinismisoclinic class of #509
automorphism?
homologyAbelianization (H1) = C23×C157 · Schur multiplier (H2) = C22

Aliases

direct product#509×C157

Subgroups

subgroupG/H
center, socleC2×C157C2×D8
commutator, Frattini, cosocleC8C23×C157
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C157 ◁ C2×C4×C157 ◁ C2×C8×C157 ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,ℤ/16)×C157, #2190×C157, #2192×C157, …
maximal normal subgroup ofAGL(1,ℤ/16)×C157, #2190×C157, #2192×C157, …
maximal quotient of#2139×C157, #2140×C157, #2159×C157, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 190);