Finite Group Databasebeta

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D19×D345 #39910778

order26220
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD19×D345
unambiguous semidirect product(C3×D19)⋊D115
unambiguous semidirect product(C5×D19)⋊D69
unambiguous semidirect product(C23×D19)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C19×C23 ⋊ C22
HallC5×C19×C23 ⋊ C2×D3
HallC3×C19×C23 ⋊ C2×D5
HallC19×C23 ⋊ C2×D15
HallC3×C5×C23 ⋊ C2×D19
HallC3×C5×C19 ⋊ C2×D23
HallC5×C23 ⋊ D3×D19
HallC5×C19 ⋊ C2×D69
HallC3×C23 ⋊ D5×D19
HallC3×C19 ⋊ C2×D115
SylowC23 ⋊ D15×D19
SylowC19 ⋊ C2×D345
HallC3×C5 ⋊ D19×D23
SylowC5 ⋊ D19×D69
SylowC3 ⋊ D19×D115

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C19×C23C22
LCSG ▷ C3×C5×C19×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6555

Conjugacy classes & character table

1914 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 68);