Finite Group Databasebeta

C2×#14538075 #17900754

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#14538075

Splittings

FittingC23×Q16×C17 ⋊ C2
SylowC17 ⋊ C2×#3011

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC23×Q16×C17C2
socleC23×C17C22×D4
prime radicalC22×#10587694C2
hypercenterC23×Q16D17
hypocenterC17C2×#3011
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

4718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1035998);