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D17×#471 #14538479

order2176
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD17×#471

Splittings

FittingC17×#471 ⋊ C2
SylowC17 ⋊ C2×#471

Subgroups

subgroupG/H
centerC2#121×D17
commutator, cosocleC2×C4×C17C24
FrattiniC2×C4C23×D17
FittingC17×#471C2
socleC2×C17C2×#121
prime radicalAGL(1,ℤ/8)×D17C2
hypercenter#471D17
hypocenterC17C2×#471
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D17×#471, D17×#3067, D17×#3068, …
maximal normal subgroup ofC2×D17×#471, D17×#3067, D17×#3068, …
maximal quotient ofD17×#1665, D17×#1671, D17×#1681, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 14205);