Finite Group Databasebeta

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C2×C3×C5×D5×C11 #15693223

order3300
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

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

Splittings

Fitting, socleC2×C3×C52×C11 ⋊ C2
derivedC5 ⋊ C22×C3×C5×C11
HallC3×C52×C11 ⋊ C22
HallC52×C11 ⋊ C22×C3
HallC3×C52 ⋊ C22×C11
SylowC52 ⋊ C22×C3×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11D5
commutator, cosocle, hypocenterC5C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C52×C11C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C5×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

1320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D5×C11×AGL(1,𝔽7), C2×C5×C11×C5⋊AGL(1,𝔽7), C2×C5×D5×C11×ΓL(1,𝔽8), …
maximal normal subgroup ofC2×C3×C5×C7×D5×C11, C2×C3×C5×D5×C121, C2×C3×C5×D5×C112
maximal quotient ofC5×D5×C11×AGL(1,𝔽7), C2×C5×C11×C5⋊AGL(1,𝔽7), C2×C5×D5×C11×ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 143);