Finite Group Databasebeta

C2×#14545968 #17983059

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14545968

Splittings

SylowC17 ⋊ C2×#2117

Subgroups

subgroupG/H
centerC22C2×C22⋊#3633
commutatorC4×C17C23×C8
FrattiniC4C23×#3633
FittingC22×Q8×C17C8
socleC22×C17C2×C22⋊C8
prime radicalC22×#63256C4
cosocle#63242C24
hypercenterC22×Q8#3633
hypocenterC17C2×#2117
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118303);