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C19⋊C3×C23⋊AGL(1,𝔽5) #39910740

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

Aliases

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

Splittings

Fitting, socle, derived, HallC5×C19×C23 ⋊ C3×C4
HallC19×C23⋊AGL(1,𝔽5) ⋊ C3
HallC5×C23×C19⋊C3 ⋊ C4
HallC23×C19⋊C3 ⋊ AGL(1,𝔽5)
HallC19×C23 ⋊ C3×AGL(1,𝔽5)
HallC5×C19⋊C3 ⋊ Dic23
HallC5×C23 ⋊ C4×C19⋊C3
HallC5×C19 ⋊ C3×Dic23
SylowC23 ⋊ AGL(1,𝔽5)×C19⋊C3
SylowC19 ⋊ C3×C23⋊AGL(1,𝔽5)
SylowC5 ⋊ C19⋊C3×Dic23

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C19×C23C3×C4
prime radicalD5×C23×C19⋊C3C2
cosocleD5×C19×C23C2×C3
LCSG ▷ C5×C19×C23
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2185

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 30);