Finite Group Databasebeta

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C11×(C3⋊D3)⋊D65 #38788250

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

Aliases

direct productC11×(C3⋊D3)⋊D65
unambiguous semidirect product(C3⋊D3)⋊(C11×D65)

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C22
derived, HallC32×C5×C13 ⋊ C22×C11
HallC32×C11×C13 ⋊ C2×D5
HallC5×C11×C13 ⋊ D32
HallC32×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ (C3⋊D3)⋊D5
HallC32×C13 ⋊ C2×D5×C11
HallC32×C11 ⋊ C2×D65
HallC5×C13 ⋊ D32×C11
HallC5×C11 ⋊ (C3⋊D3)⋊D13
HallC32×C5 ⋊ C2×C11×D13
SylowC13 ⋊ C11×(C3⋊D3)⋊D5
SylowC32 ⋊ C2×C11×D65
SylowC5 ⋊ C11×(C3⋊D3)⋊D13

Subgroups

subgroupG/H
center, hypercenterC11(C3⋊D3)⋊D65
commutator, cosocle, hypocenterC32×C5×C13C22×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C5×C13
UCSC1 ◁ C11

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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

2211 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 481);