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C4×C52×C49⋊C3 #28412876

order14700
isoclinismisoclinic class of C49⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52×C49⋊C3
unambiguous semidirect product(C4×C49)⋊(C3×C52)
unambiguous semidirect product(C4×C5×C49)⋊(C3×C5)

Splittings

Fitting, HallC4×C52×C49 ⋊ C3
derived, SylowC49 ⋊ C3×C4×C52
HallC52×C49 ⋊ C3×C4
HallC4×C49 ⋊ C3×C52

Subgroups

subgroupG/H
center, hypercenterC4×C52C49⋊C3
commutator, hypocenterC49C3×C4×C52
FrattiniC2×C7C2×C52×ΓL(1,𝔽8)
FittingC4×C52×C49C3
socleC2×C52×C7C2×ΓL(1,𝔽8)
prime radicalC2×C52×C49⋊C3C2
cosocleC2×C49C2×C3×C52
LCSG ▷ C49
UCSC1 ◁ C4×C52

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 55);