Finite Group Databasebeta

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D3×D2145 #38788237

order25740
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD3×D2145
unambiguous semidirect product(C3×D3)⋊D715
unambiguous semidirect product(C5×D3)⋊D429
unambiguous semidirect product(D3×C11)⋊D195
unambiguous semidirect product(D3×C13)⋊D165

Splittings

Fitting, socle, derived, HallC32×C5×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C2×D5
HallC5×C11×C13 ⋊ D32
HallC32×C5×C13 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ D3×D15
HallC32×C13 ⋊ C2×D55
HallC32×C11 ⋊ C2×D65
HallC5×C13 ⋊ D3×D33
HallC5×C11 ⋊ D3×D39
HallC32×C5 ⋊ C2×D143
SylowC13 ⋊ D3×D165
SylowC11 ⋊ D3×D195
SylowC32 ⋊ C2×D715
SylowC5 ⋊ D3×D429

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C11×C13C22
LCSG ▷ C32×C5×C11×C13
UCSC1

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 4290

Conjugacy classes & character table

3222 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 468);