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H(3,ℤ/4)×Dic17 #16939487

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C43

Aliases

direct productH(3,ℤ/4)×Dic17

Splittings

SylowC17 ⋊ C4×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C42×D17
commutatorC4×C17C43
FrattiniC23×C4C22×D17
FittingC2×C17×H(3,ℤ/4)C2
socleC22×C17C2×#95
prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenterC2×H(3,ℤ/4)D17
hypocenterC17C4×H(3,ℤ/4)
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 74731);