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C4×C17×C49⋊C3 #23756102

order9996
isoclinismisoclinic class of C49⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×C49⋊C3
unambiguous semidirect product(C4×C49)⋊(C3×C17)
unambiguous semidirect product(C4×C17×C49)⋊C3

Splittings

Fitting, HallC4×C17×C49 ⋊ C3
derived, SylowC49 ⋊ C3×C4×C17
HallC17×C49 ⋊ C3×C4
HallC4×C49 ⋊ C3×C17

Subgroups

subgroupG/H
center, hypercenterC4×C17C49⋊C3
commutator, hypocenterC49C3×C4×C17
FrattiniC2×C7C2×C17×ΓL(1,𝔽8)
FittingC4×C17×C49C3
socleC2×C7×C17C2×ΓL(1,𝔽8)
prime radicalC2×C17×C49⋊C3C2
cosocleC2×C49C2×C3×C17
LCSG ▷ C49
UCSC1 ◁ C4×C17

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofDic3×C17×C49⋊C3, C3×C4×C17×C49⋊C3
maximal normal subgroup ofC3×C4×C17×C49⋊C3
maximal quotient ofC4×C17×C49⋊C9, Dic3×C17×C49⋊C3, C3×C4×C17×C49⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9996, 5);