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C2×C11×D7×C25 #21440367

order7700
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C22×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D7×C25
unambiguous semidirect productC7⋊(C22×C11×C25)
unambiguous semidirect product(C2×C7)⋊(C2×C11×C25)

Splittings

FittingC2×C7×C11×C25 ⋊ C2
derived, SylowC7 ⋊ C22×C11×C25
HallC7×C11×C25 ⋊ C22
HallC7×C25 ⋊ C22×C11
HallC7×C11 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C11×C25D7
commutator, hypocenterC7C22×C11×C25
FrattiniC5C2×C5×C11×D7
FittingC2×C7×C11×C25C2
socleC2×C5×C7×C11C2×C5
LCSG ▷ C7
UCSC1 ◁ C2×C11×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2750 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C25×AGL(1,𝔽7), D3×C11×D7×C25, C2×C3×C11×D7×C25, …
maximal normal subgroup ofC2×C11×C25×AGL(1,𝔽7), C2×C3×C11×D7×C25
maximal quotient ofD3×C11×D7×C25, C2×C3×C11×D7×C25, C2×C11×C25×D21

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 31);