Finite Group Databasebeta

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D11×C3⋊D195 #38788279

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

Aliases

direct productD11×C3⋊D195
unambiguous semidirect product(C3×D11)⋊D195
unambiguous semidirect product(C5×D11)⋊(C3⋊D39)
unambiguous semidirect product(C13×D11)⋊(C3⋊D15)

Splittings

Fitting, socle, derived, 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 ⋊ D5×D11
HallC32×C11 ⋊ C2×D65
HallC5×C13 ⋊ C3⋊D3×D11
HallC5×C11 ⋊ C2×C3⋊D39
HallC32×C5 ⋊ D11×D13
SylowC13 ⋊ D11×C3⋊D15
SylowC11 ⋊ C2×C3⋊D195
SylowC32 ⋊ D11×D65
SylowC5 ⋊ D11×C3⋊D39

Subgroups

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

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

normal subgroups only

This group has 240 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) = 6435

Conjugacy classes & character table

2058 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 510);