Finite Group Databasebeta

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C5×C19⋊C3×Dic23 #39910728

order26220
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C19⋊C3×Dic23
unambiguous semidirect productC23⋊(C4×C5×C19⋊C3)
unambiguous semidirect product(C19×Dic23)⋊(C3×C5)
unambiguous semidirect product(C5×C19×Dic23)⋊C3

Splittings

derived, HallC19×C23 ⋊ C3×C4×C5
HallC5×C19×Dic23 ⋊ C3
HallC5×C23×C19⋊C3 ⋊ C4
HallC5×C19×C23 ⋊ C3×C4
HallC19×Dic23 ⋊ C3×C5
HallC23×C19⋊C3 ⋊ C4×C5
HallC5×C23 ⋊ C4×C19⋊C3
HallC5×C19 ⋊ C3×Dic23
SylowC23 ⋊ C4×C5×C19⋊C3
SylowC19 ⋊ C3×C5×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C5D23×C19⋊C3
commutator, hypocenterC19×C23C3×C4×C5
FrattiniC2C5×D23×C19⋊C3
Fitting, socleC2×C5×C19×C23C2×C3
prime radicalC2×C5×C23×C19⋊C3C2
cosocleC2×C19×C23C2×C3×C5
LCSG ▷ C19×C23
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8740

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 18);