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C4×C7×C7⋊(C52⋊C3) #28413192

order14700
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C5

Aliases

direct productC4×C7×C7⋊(C52⋊C3)
unambiguous semidirect product(C4×C7)⋊(C7×C52⋊C3)
unambiguous semidirect product(C4×C52)⋊(C7×ΓL(1,𝔽8))

Splittings

Fitting, HallC4×C52×C72 ⋊ C3
derivedC52×C7 ⋊ C3×C4×C7
HallC52×C72 ⋊ C3×C4
HallC4×C72 ⋊ C52⋊C3
HallC4×C52 ⋊ C7×ΓL(1,𝔽8)
SylowC72 ⋊ C4×C52⋊C3
SylowC52 ⋊ C4×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC4×C7C7⋊(C52⋊C3)
commutator, hypocenterC52×C7C3×C4×C7
FrattiniC2C2×C7×C7⋊(C52⋊C3)
FittingC4×C52×C72C3
socleC2×C52×C72C2×C3
prime radicalC2×C7×C7⋊(C52⋊C3)C2
cosocleC2×C52×C7C2×C3×C7
LCSG ▷ C52×C7
UCSC1 ◁ C4×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1708 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 371);