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C17×#10596874 #23756142

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

Aliases

direct productC17×#10596874

Splittings

derived, SylowC72 ⋊ C3×C4×C17
HallC17×C7⋊Dic7 ⋊ C3
HallC17×#3861 ⋊ C4
HallC72×C17 ⋊ C3×C4
HallC7⋊Dic7 ⋊ C3×C17
Hall#3861 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17#64424
commutator, hypocenterC72C3×C4×C17
FrattiniC2C17×#64424
Fitting, socleC2×C72×C17C2×C3
prime radicalC2×C17×#3861C2
cosocleC2×C72C2×C3×C17
LCSG ▷ C72
UCSC1 ◁ C2×C17

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC17×ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊C4), C3×C17×#10596874, C17×C3⋊#10596874
maximal normal subgroup ofC17×ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊C4), C3×C17×#10596874
maximal quotient ofC17×#13183533, C3×C17×#10596874, C17×C3⋊#10596874

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9996, 45);