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C2×D3×C11×C25 #15693115

order3300
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C22×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×D3×C11×C25
unambiguous semidirect productC3⋊(C22×C11×C25)
unambiguous semidirect product(C2×C3)⋊(C2×C11×C25)

Splittings

FittingC2×C3×C11×C25 ⋊ C2
derived, SylowC3 ⋊ C22×C11×C25
HallC3×C11×C25 ⋊ C22
HallC3×C25 ⋊ C22×C11
HallC3×C11 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C11×C25D3
commutator, hypocenterC3C22×C11×C25
FrattiniC5C2×C5×D3×C11
FittingC2×C3×C11×C25C2
socleC2×C3×C5×C11C2×C5
prime radicalC2×C5×D3×C11C5
cosocleC3×C5C22×C5×C11
LCSG ▷ C3
UCSC1 ◁ C2×C11×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1650

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C11×D7×C25, C2×D3×C7×C11×C25, C2×C11×C25×D21, …
maximal normal subgroup ofC2×D3×C7×C11×C25, C2×D3×C25×C121, C2×D3×C112×C25
maximal quotient ofD3×C11×D7×C25, C2×D3×C7×C11×C25, C2×C11×C25×D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 35);