Finite Group Databasebeta

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C2×C3×D2145 #38788315

order25740
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D2145
unambiguous semidirect product(C2×C3)⋊(C3×D715)
unambiguous semidirect product(C2×C5)⋊(C3×D429)
unambiguous semidirect product(C2×C11)⋊(C3×D195)

Splittings

Fitting, socleC2×C32×C5×C11×C13 ⋊ C2
derivedC3×C5×C11×C13 ⋊ C22×C3
HallC32×C5×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C2×D5
HallC5×C11×C13 ⋊ C2×C3×D3
HallC32×C5×C13 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C3×D15
HallC32×C13 ⋊ C2×D55
HallC32×C11 ⋊ C2×D65
HallC5×C13 ⋊ C2×C3×D33
HallC5×C11 ⋊ C2×C3×D39
HallC32×C5 ⋊ C2×D143
SylowC13 ⋊ C2×C3×D165
SylowC11 ⋊ C2×C3×D195
SylowC32 ⋊ C2×D715
SylowC5 ⋊ C2×C3×D429

Subgroups

subgroupG/H
center, hypercenterC2×C3D2145
commutator, cosocle, hypocenterC3×C5×C11×C13C22×C3
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C3×C5×C11×C13
UCSC1 ◁ C2×C3

176 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 8580

Conjugacy classes & character table

6444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 546);