Finite Group Databasebeta

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C2×C5×C11×D15 #15693229

order3300
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C11×D15
unambiguous semidirect product(C2×C3)⋊(C5×D5×C11)
unambiguous semidirect product(C2×C5)⋊(C5×D3×C11)

Splittings

Fitting, socleC2×C3×C52×C11 ⋊ C2
derivedC3×C5 ⋊ C22×C5×C11
HallC3×C52×C11 ⋊ C22
HallC52×C11 ⋊ C2×D3
HallC3×C52 ⋊ C22×C11
HallC3×C11 ⋊ C2×C5×D5
SylowC52 ⋊ C2×D3×C11
SylowC3 ⋊ C2×C5×D5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D15
commutator, cosocle, hypocenterC3×C5C22×C5×C11
FrattiniC1G
Fitting, socleC2×C3×C52×C11C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C5×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C11×D7×D15, C2×C5×C7×C11×D15, C2×C5×C11×D105, …
maximal normal subgroup ofC2×C5×C7×C11×D15, C2×C5×D15×C121, C2×C5×C112×D15
maximal quotient ofC5×C11×D7×D15, C2×C5×C7×C11×D15, C2×C5×C11×D105, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 149);