Finite Group Databasebeta

← Prev (#38788311) Next (#38788313) →

C2×C3×C11×C13×D15 #38788312

order25740
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11×C13×D15
unambiguous semidirect product(C2×C3)⋊(C3×D5×C11×C13)
unambiguous semidirect product(C2×C5)⋊(C3×D3×C11×C13)

Splittings

Fitting, socleC2×C32×C5×C11×C13 ⋊ C2
derivedC3×C5 ⋊ C22×C3×C11×C13
HallC32×C5×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C2×D5
HallC5×C11×C13 ⋊ C2×C3×D3
HallC32×C5×C13 ⋊ C22×C11
HallC32×C5×C11 ⋊ C22×C13
HallC32×C13 ⋊ C2×D5×C11
HallC32×C11 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×C3×D3×C11
HallC5×C11 ⋊ C2×C3×D3×C13
HallC32×C5 ⋊ C22×C11×C13
SylowC32 ⋊ C2×D5×C11×C13
SylowC5 ⋊ C2×C3×D3×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C13D15
commutator, cosocle, hypocenterC3×C5C22×C3×C11×C13
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C11×C13

176 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 88 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

7722 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 543);