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C2×C7×D7×C121 #37557370

order23716
automorphism?
homologyAbelianization (H1) = C22×C7×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D7×C121
unambiguous semidirect productC7⋊(C22×C7×C121)
unambiguous semidirect product(C2×C7)⋊(C2×C7×C121)

Splittings

FittingC2×C72×C121 ⋊ C2
derivedC7 ⋊ C22×C7×C121
HallC72×C121 ⋊ C22
SylowC72 ⋊ C22×C121

Subgroups

subgroupG/H
center, hypercenterC2×C7×C121D7
commutator, hypocenterC7C22×C7×C121
FrattiniC11C2×C7×C11×D7
FittingC2×C72×C121C2
socleC2×C72×C11C2×C11
prime radicalC2×C7×C11×D7C11
cosocleC7×C11C22×C7×C11
LCSG ▷ C7
UCSC1 ◁ C2×C7×C121

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3388

Conjugacy classes & character table

8470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23716, 33);