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C17×AGL(1,𝔽23) #22575263

order8602
isoclinismisoclinic class of AGL(1,𝔽23)
automorphism?
homologyAbelianization (H1) = C2×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C11×C17)
unambiguous semidirect product(C23⋊C11)⋊(C2×C17)
unambiguous semidirect product(C17×D23)⋊C11

Splittings

Fitting, socle, HallC17×C23 ⋊ C2×C11
derived, SylowC23 ⋊ C2×C11×C17
HallC17×C23⋊C11 ⋊ C2
HallC17×D23 ⋊ C11
HallC23⋊C11 ⋊ C2×C17
HallD23 ⋊ C11×C17

Subgroups

subgroupG/H
center, hypercenterC17AGL(1,𝔽23)
commutator, hypocenterC23C2×C11×C17
FrattiniC1G
Fitting, socleC17×C23C2×C11
LCSG ▷ C23
UCSC1 ◁ C17

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

391 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD17×AGL(1,𝔽23), C2×C17×AGL(1,𝔽23), C3×C17×AGL(1,𝔽23), …
maximal normal subgroup ofD17×AGL(1,𝔽23), C2×C17×AGL(1,𝔽23), C3×C17×AGL(1,𝔽23)
maximal quotient ofC17×Dic23⋊C11, C2×C17×AGL(1,𝔽23), C3×C17×AGL(1,𝔽23), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8602, 10);