Finite Group Databasebeta

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D5×D1197 #37561022

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

Aliases

direct productD5×D1197
unambiguous semidirect product(C7×D5)⋊D171
unambiguous semidirect product(C9×D5)⋊D133
unambiguous semidirect product(D5×C19)⋊D63

Splittings

Fitting, derived, HallC5×C7×C9×C19 ⋊ C22
HallC7×C9×C19 ⋊ C2×D5
HallC5×C9×C19 ⋊ C2×D7
HallC5×C7×C19 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D19
HallC9×C19 ⋊ D5×D7
HallC7×C19 ⋊ D5×D9
HallC5×C19 ⋊ C2×D63
HallC7×C9 ⋊ D5×D19
HallC5×C9 ⋊ C2×D133
HallC5×C7 ⋊ C2×D171
SylowC19 ⋊ D5×D63
SylowC9 ⋊ D5×D133
SylowC7 ⋊ D5×D171
SylowC5 ⋊ C2×D1197

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C7×C9×C19C22
FrattiniC3D5×D399
socleC3×C5×C7×C19C2×D3
LCSG ▷ C5×C7×C9×C19
UCSC1

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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, 154);