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C2×C11×(C5⋊D5)⋊C3 #15693176

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

Aliases

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

Splittings

Fitting, socleC2×C52×C11 ⋊ C2×C3
derived, SylowC52 ⋊ C22×C3×C11
HallC2×C11×C5⋊D5 ⋊ C3
HallC11×C52⋊C3 ⋊ C22
HallC52×C11 ⋊ C22×C3
HallC2×C5⋊D5 ⋊ C3×C11
HallC52⋊C3 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52C22×C3×C11
FrattiniC1G
Fitting, socleC2×C52×C11C2×C3
LCSG ▷ C52
UCSC1 ◁ C2×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 330

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×D7⋊((C5⋊D5)⋊C3), C11×D7×(C5⋊D5)⋊C3, C2×C7×C11×(C5⋊D5)⋊C3, …
maximal normal subgroup ofC2×C7×C11×(C5⋊D5)⋊C3, C2×C121×(C5⋊D5)⋊C3, C2×C112×(C5⋊D5)⋊C3
maximal quotient ofC11×D7⋊((C5⋊D5)⋊C3), C11×D7×(C5⋊D5)⋊C3, C2×C7×C11×(C5⋊D5)⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 96);