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C23×C3⋊(C19⋊AGL(1,𝔽5)) #39910773

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

Aliases

direct productC23×C3⋊(C19⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C23×C19⋊AGL(1,𝔽5))
unambiguous semidirect productC19⋊(C23×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C19×C23 ⋊ C4
derived, HallC3×C5×C19 ⋊ C4×C23
HallC5×C19×C23 ⋊ Dic3
HallC3×C19×C23 ⋊ AGL(1,𝔽5)
HallC19×C23 ⋊ ΓL(1,𝔽16)
HallC3×C5×C23 ⋊ Dic19
HallC5×C23 ⋊ Dic57
HallC5×C19 ⋊ Dic3×C23
HallC3×C23 ⋊ C19⋊AGL(1,𝔽5)
HallC3×C19 ⋊ AGL(1,𝔽5)×C23
SylowC19 ⋊ C23×ΓL(1,𝔽16)
HallC3×C5 ⋊ C23×Dic19
SylowC5 ⋊ C23×Dic57
SylowC3 ⋊ C23×C19⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC23C3⋊(C19⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C19C4×C23
FrattiniC1G
Fitting, socleC3×C5×C19×C23C4
prime radicalC3×D5×C19×C23C2
cosocleC3×D5×C19C2×C23
LCSG ▷ C3×C5×C19
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6555

Conjugacy classes & character table

2691 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 63);