Finite Group Databasebeta

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C2×C3×D5×C23⋊C11 #29503262

order15180
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D5×C23⋊C11
unambiguous semidirect productC5⋊(C22×C3×C23⋊C11)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C23⋊C11)
unambiguous semidirect product(C2×D5×C23)⋊(C3×C11)
unambiguous semidirect product(C2×C3×D5×C23)⋊C11

Splittings

Fitting, socleC2×C3×C5×C23 ⋊ C2×C11
derived, HallC5×C23 ⋊ C22×C3×C11
HallC3×C5×C23⋊C11 ⋊ C22
HallC2×C3×D5×C23 ⋊ C11
HallC5×C23⋊C11 ⋊ C22×C3
HallC2×D5×C23 ⋊ C3×C11
HallC3×C5×C23 ⋊ C22×C11
HallC3×C23 ⋊ C2×D5×C11
SylowC23 ⋊ C2×C3×D5×C11
HallC3×C5 ⋊ C22×C23⋊C11
SylowC5 ⋊ C22×C3×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×C23⋊C11
commutator, cosocle, hypocenterC5×C23C22×C3×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C23C2×C11
LCSG ▷ C5×C23
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 690

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 48);