Finite Group Databasebeta

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C5×C23×(C19⋊C3)⋊C4 #39910729

order26220
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×(C19⋊C3)⋊C4
unambiguous semidirect product(C19⋊C3)⋊(C4×C5×C23)
unambiguous semidirect productDic19⋊(C3×C5×C23)
unambiguous semidirect product(C5×Dic19)⋊(C3×C23)
unambiguous semidirect product(C23×Dic19)⋊(C3×C5)
unambiguous semidirect product(C5×C23×Dic19)⋊C3

Splittings

derived, SylowC19 ⋊ C3×C4×C5×C23
HallC5×C23×Dic19 ⋊ C3
HallC5×C23×C19⋊C3 ⋊ C4
HallC5×C19×C23 ⋊ C3×C4
HallC23×Dic19 ⋊ C3×C5
HallC23×C19⋊C3 ⋊ C4×C5
HallC19×C23 ⋊ C3×C4×C5
HallC5×Dic19 ⋊ C3×C23
HallC5×C19⋊C3 ⋊ C4×C23
HallC5×C19 ⋊ C3×C4×C23
HallDic19 ⋊ C3×C5×C23
HallC19⋊C3 ⋊ C4×C5×C23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C23D19⋊C3
commutator, hypocenterC19C3×C4×C5×C23
FrattiniC2C5×C23×D19⋊C3
Fitting, socleC2×C5×C19×C23C2×C3
prime radicalC2×C5×C23×C19⋊C3C2
cosocleC2×C19C2×C3×C5×C23
LCSG ▷ C19
UCSC1 ◁ C2×C5×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8740

Conjugacy classes & character table

2070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 19);