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C17×(C49⋊C3)⋊C4 #23756100

order9996
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×(C49⋊C3)⋊C4
unambiguous semidirect product(C49⋊C3)⋊(C4×C17)
unambiguous semidirect productDic49⋊(C3×C17)
unambiguous semidirect product(C17×Dic49)⋊C3

Splittings

derived, SylowC49 ⋊ C3×C4×C17
HallC17×Dic49 ⋊ C3
HallC17×C49⋊C3 ⋊ C4
HallC17×C49 ⋊ C3×C4
HallDic49 ⋊ C3×C17
HallC49⋊C3 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D49⋊C3
commutator, hypocenterC49C3×C4×C17
FrattiniC2×C7C17×AGL(1,𝔽7)
FittingC2×C17×C49C2×C3
socleC2×C7×C17AGL(1,𝔽7)
prime radicalC2×C17×C49⋊C3C2
cosocleC2×C49C2×C3×C17
LCSG ▷ C49
UCSC1 ◁ C2×C17

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C17×(C49⋊C3)⋊C4, C17×C3⋊((C49⋊C3)⋊C4)
maximal normal subgroup ofC3×C17×(C49⋊C3)⋊C4
maximal quotient ofC17×Dic49⋊C9, C3×C17×(C49⋊C3)⋊C4, C17×C3⋊((C49⋊C3)⋊C4)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9996, 3);