Finite Group Databasebeta

C16×C4⋊Dic17 #16949666

order4352
isoclinismisoclinic class of Dic34
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC16×C4⋊Dic17

Splittings

SylowC17 ⋊ C16×C4⋊C4

Subgroups

subgroupG/H
centerC22×C16C2×D17
commutatorC2×C17C2×C4×C16
FrattiniC22×C8C22×D17
FittingC2×C4×C16×C17C2
socle, prime radicalC23×C17C22×C8
cosocleC22×C8×C17C23
hypercenterC2×C4×C16D17
hypocenterC17C16×C4⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C16 ◁ C2×C4×C16

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84910);