Finite Group Databasebeta

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C22×C9×AGL(1,𝔽23) #72218995

order18216
isoclinismisoclinic class of AGL(1,𝔽23)
automorphism?
homologyAbelianization (H1) = C23×C9×C11 · Schur multiplier (H2) = C23

Aliases

direct productC22×C9×AGL(1,𝔽23)

Splittings

FittingC22×C9×C23 ⋊ C2×C11
derived, SylowC23 ⋊ C23×C9×C11
HallC9×C23⋊C11 ⋊ C23
HallC22×C9×D23 ⋊ C11
HallC23⋊C11 ⋊ C23×C9
HallC9×C23 ⋊ C23×C11
HallC22×D23 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC22×C9AGL(1,𝔽23)
commutator, hypocenterC23C23×C9×C11
FrattiniC3C22×C3×AGL(1,𝔽23)
FittingC22×C9×C23C2×C11
socleC22×C3×C23C2×C3×C11
prime radicalC22×C3×AGL(1,𝔽23)C3
cosocleC3×C23C23×C3×C11
LCSG ▷ C23
UCSC1 ◁ C22×C9

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

automorphism group ofC19×Dic23, C2×C19×D23

GAP

Past the SmallGroups library coverage — no SmallGroups id.