Finite Group Databasebeta

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C2×C11×D195 #22575184

order8580
isoclinismisoclinic class of D195
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D195
unambiguous semidirect product(C2×C3)⋊(C11×D65)
unambiguous semidirect product(C2×C5)⋊(C11×D39)
unambiguous semidirect product(C2×C13)⋊(C11×D15)

Splittings

Fitting, socleC2×C3×C5×C11×C13 ⋊ C2
derived, HallC3×C5×C13 ⋊ C22×C11
HallC3×C5×C11×C13 ⋊ C22
HallC5×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D5
HallC3×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×D15
HallC5×C13 ⋊ C2×D3×C11
HallC5×C11 ⋊ C2×D39
HallC3×C13 ⋊ C2×D5×C11
HallC3×C11 ⋊ C2×D65
HallC3×C5 ⋊ C2×C11×D13
SylowC13 ⋊ C2×C11×D15
SylowC5 ⋊ C2×C11×D39
SylowC3 ⋊ C2×C11×D65

Subgroups

subgroupG/H
center, hypercenterC2×C11D195
commutator, hypocenterC3×C5×C13C22×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C2×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×D585, C2×C11×C3⋊(C5⋊(D13⋊C3)), D3×C11×D195, …
maximal normal subgroup ofC2×C11×C3⋊(C5⋊(D13⋊C3)), C2×C3×C11×D195
maximal quotient ofC2×C11×D585, D3×C11×D195, C2×C3×C11×D195, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 156);