Finite Group Databasebeta

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C2×D3×C23×C11⋊C5 #29503281

order15180
automorphism?
homologyAbelianization (H1) = C22×C5×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×D3×C23×C11⋊C5
unambiguous semidirect productC3⋊(C22×C23×C11⋊C5)
unambiguous semidirect product(C2×C3)⋊(C2×C23×C11⋊C5)
unambiguous semidirect product(C2×D3×C11)⋊(C5×C23)
unambiguous semidirect product(C2×D3×C11×C23)⋊C5

Splittings

Fitting, socleC2×C3×C11×C23 ⋊ C2×C5
derived, HallC3×C11 ⋊ C22×C5×C23
HallC3×C23×C11⋊C5 ⋊ C22
HallC2×D3×C11×C23 ⋊ C5
HallC3×C11×C23 ⋊ C22×C5
HallC11×C23 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C22×C23
HallC2×D3×C11 ⋊ C5×C23
HallC3×C23 ⋊ C22×C11⋊C5
SylowC11 ⋊ C2×C5×D3×C23
SylowC3 ⋊ C22×C23×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C23D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C22×C5×C23
FrattiniC1G
Fitting, socleC2×C3×C11×C23C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1518

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 67);