Finite Group Databasebeta

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C2×C5×C23×D33 #29503333

order15180
isoclinismisoclinic class of D33
automorphism?
homologyAbelianization (H1) = C22×C5×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C23×D33
unambiguous semidirect product(C2×C3)⋊(C5×D11×C23)

Splittings

Fitting, socleC2×C3×C5×C11×C23 ⋊ C2
derived, HallC3×C11 ⋊ C22×C5×C23
HallC3×C5×C11×C23 ⋊ C22
HallC5×C11×C23 ⋊ C2×D3
HallC3×C11×C23 ⋊ C22×C5
HallC3×C5×C23 ⋊ C2×D11
HallC11×C23 ⋊ C2×C5×D3
HallC3×C5×C11 ⋊ C22×C23
HallC3×C23 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×D3×C23
HallC3×C5 ⋊ C2×D11×C23
SylowC11 ⋊ C2×C5×D3×C23
SylowC3 ⋊ C2×C5×D11×C23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C23D33
commutator, cosocle, hypocenterC3×C11C22×C5×C23
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C23C2
LCSG ▷ C3×C11
UCSC1 ◁ C2×C5×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7590

Conjugacy classes & character table

4140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 119);