Finite Group Databasebeta

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C2×C3×C5×D429 #38788311

order25740
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D429
unambiguous semidirect product(C2×C3)⋊(C3×C5×D143)

Splittings

Fitting, socleC2×C32×C5×C11×C13 ⋊ C2
derivedC3×C11×C13 ⋊ C22×C3×C5
HallC32×C5×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C22×C5
HallC5×C11×C13 ⋊ C2×C3×D3
HallC32×C5×C13 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C3×C5×D3
HallC32×C13 ⋊ C2×C5×D11
HallC32×C11 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×C3×D33
HallC5×C11 ⋊ C2×C3×D39
HallC32×C5 ⋊ C2×D143
SylowC13 ⋊ C2×C3×C5×D33
SylowC11 ⋊ C2×C3×C5×D39
SylowC32 ⋊ C2×C5×D143

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D429
commutator, cosocle, hypocenterC3×C11×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2×C3×C5

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

normal subgroups only

This group has 176 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) = 8580

Conjugacy classes & character table

6480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 542);