Finite Group Databasebeta

C2×Q16×C22⋊D17 #17909595

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×Q16×C22⋊D17

Splittings

FittingC23×Q16×C17 ⋊ C2
SylowC17 ⋊ C2×D4×Q16

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC23×Q16×C17C2
socleC23×C17C22×D4
prime radicalC22×C22⋊D17D4
hypercenterC23×Q16D17
hypocenterC17C2×D4×Q16
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

2742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1044839);