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C2×M16×Dic17 #14537191

order2176
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×Dic17

Splittings

SylowC17 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×D17
commutatorC2×C17C22×C42
FrattiniC2×C4C23×D17
FittingC22×M16×C17C2
socleC23×C17C22×C4
prime radicalC24×C17C2×C4
cosocleC2×C4×C17C24
hypercenterC22×M16D17
hypocenterC17C2×C4×M16
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×M16

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

Relationships

maximal subgroup ofH(3,ℤ/4)×Dic17, #338×Dic17, #339×Dic17, …
maximal normal subgroup ofH(3,ℤ/4)×Dic17, #338×Dic17, #339×Dic17, …
maximal quotient ofC2×M16×#3622, C2×#14527065, C2×#14527071, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 12917);