Finite Group Databasebeta

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D5×C3⋊D399 #37561609

order23940
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3

Aliases

direct productD5×C3⋊D399
unambiguous semidirect product(C3×D5)⋊D399
unambiguous semidirect product(C7×D5)⋊(C3⋊D57)
unambiguous semidirect product(D5×C19)⋊(C3⋊D21)

Splittings

Fitting, socle, derived, HallC32×C5×C7×C19 ⋊ C22
HallC32×C7×C19 ⋊ C2×D5
HallC32×C5×C19 ⋊ C2×D7
HallC5×C7×C19 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D19
HallC32×C19 ⋊ D5×D7
HallC7×C19 ⋊ D5×C3⋊D3
HallC5×C19 ⋊ C2×C3⋊D21
HallC32×C7 ⋊ D5×D19
HallC32×C5 ⋊ C2×D133
HallC5×C7 ⋊ C2×C3⋊D57
SylowC19 ⋊ D5×C3⋊D21
SylowC32 ⋊ D5×D133
SylowC7 ⋊ D5×C3⋊D57
SylowC5 ⋊ C2×C3⋊D399

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C19C22
LCSG ▷ C32×C5×C7×C19
UCSC1

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5985

Conjugacy classes & character table

2400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 741);