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C11×D795 #31775820

order17490
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D795
unambiguous semidirect productC3⋊(C11×D265)
unambiguous semidirect productC5⋊(C11×D159)
unambiguous semidirect productC53⋊(C11×D15)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, HallC3×C5×C53 ⋊ C2×C11
HallC5×C11×C53 ⋊ D3
HallC3×C11×C53 ⋊ D5
HallC11×C53 ⋊ D15
HallC5×C53 ⋊ D3×C11
HallC3×C5×C11 ⋊ D53
HallC3×C53 ⋊ D5×C11
HallC5×C11 ⋊ D159
SylowC53 ⋊ C11×D15
HallC3×C11 ⋊ D265
HallC3×C5 ⋊ C11×D53
SylowC5 ⋊ C11×D159
SylowC3 ⋊ C11×D265

Subgroups

subgroupG/H
center, hypercenterC11D795
commutator, cosocle, hypocenterC3×C5×C53C2×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C3×C5×C53
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

4389 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D15×D53, D11×D795, D583⋊D15, …
maximal normal subgroup ofC11×D15×D53, D11×D795, D583⋊D15, …
maximal quotient ofC11×Dic795, C2×C11×D795

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 15);