Finite Group Databasebeta

C2×#14544627 #17969206

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14544627

Splittings

FittingC23×Q8×C17 ⋊ C4
SylowC17 ⋊ C2×#1789

Subgroups

subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC23×Q8×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×#63256C2
cosocleC2×C4×D17C24
hypercenterC23×Q8#595
hypocenterC17C2×#1789
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

4102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1104450);