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C23×(C19⋊C3)⋊AGL(1,𝔽5) #39910737

order26220
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×(C19⋊C3)⋊AGL(1,𝔽5)
unambiguous semidirect product(C19⋊C3)⋊(AGL(1,𝔽5)×C23)
unambiguous semidirect product(C19⋊AGL(1,𝔽5))⋊(C3×C23)
unambiguous semidirect product(C23×C19⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, socle, HallC5×C19×C23 ⋊ C3×C4
derived, HallC5×C19 ⋊ C3×C4×C23
HallC23×C19⋊AGL(1,𝔽5) ⋊ C3
HallC5×C23×C19⋊C3 ⋊ C4
HallC23×C19⋊C3 ⋊ AGL(1,𝔽5)
HallC19×C23 ⋊ C3×AGL(1,𝔽5)
HallC19⋊AGL(1,𝔽5) ⋊ C3×C23
HallC5×C19⋊C3 ⋊ C4×C23
HallC5×C23 ⋊ (C19⋊C3)⋊C4
HallC19⋊C3 ⋊ AGL(1,𝔽5)×C23
SylowC19 ⋊ C3×AGL(1,𝔽5)×C23
SylowC5 ⋊ C23×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC23(C19⋊C3)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C19C3×C4×C23
FrattiniC1G
Fitting, socleC5×C19×C23C3×C4
prime radicalD5×C23×C19⋊C3C2
cosocleD5×C19C2×C3×C23
LCSG ▷ C5×C19
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2185

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 27);