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C13×AGL(1,𝔽5)×C23 #20238674

order5980
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C13×C23 · Schur multiplier (H2) = C1

Aliases

direct productC13×AGL(1,𝔽5)×C23

Splittings

Fitting, socle, HallC5×C13×C23 ⋊ C4
derived, SylowC5 ⋊ C4×C13×C23
HallC5×C23 ⋊ C4×C13
HallC5×C13 ⋊ C4×C23

Subgroups

subgroupG/H
center, hypercenterC13×C23AGL(1,𝔽5)
commutator, hypocenterC5C4×C13×C23
FrattiniC1G
Fitting, socleC5×C13×C23C4
LCSG ▷ C5
UCSC1 ◁ C13×C23

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1495 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C23×C13⋊C3, C3×C13×AGL(1,𝔽5)×C23, C13×C23×ΓL(1,𝔽16), …
maximal normal subgroup ofAGL(1,𝔽5)×C23×C13⋊C3, C3×C13×AGL(1,𝔽5)×C23, C5×C13×AGL(1,𝔽5)×C23
maximal quotient ofC3×C13×AGL(1,𝔽5)×C23, C13×C23×ΓL(1,𝔽16), C13×C23×#1035, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5980, 13);