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C2×D7×C17×C25 #26045385

order11900
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C22×C17×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×D7×C17×C25
unambiguous semidirect productC7⋊(C22×C17×C25)
unambiguous semidirect product(C2×C7)⋊(C2×C17×C25)

Splittings

FittingC2×C7×C17×C25 ⋊ C2
derived, SylowC7 ⋊ C22×C17×C25
HallC7×C17×C25 ⋊ C22
HallC7×C25 ⋊ C22×C17
HallC7×C17 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C17×C25D7
commutator, hypocenterC7C22×C17×C25
FrattiniC5C2×C5×D7×C17
FittingC2×C7×C17×C25C2
socleC2×C5×C7×C17C2×C5
prime radicalC2×C5×D7×C17C5
cosocleC5×C7C22×C5×C17
LCSG ▷ C7
UCSC1 ◁ C2×C17×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4250 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C17×C25×AGL(1,𝔽7), D3×D7×C17×C25, C2×C17×C25×D21, …
maximal normal subgroup ofC2×C17×C25×AGL(1,𝔽7), C2×C3×D7×C17×C25
maximal quotient ofD3×D7×C17×C25, C2×C17×C25×D21, C2×C3×D7×C17×C25

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 34);