Finite Group Databasebeta

C2×#14537203 #17897723

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#14537203

Splittings

SylowC17 ⋊ C2×#2873

Subgroups

subgroupG/H
centerC22×C4C23×D17
commutatorC2×C17C23×C42
FrattiniC2×C4C24×D17
FittingC22×C17×#117C2
socleC23×C17C23×C4
prime radicalC25×C17C2×C4
cosocleC2×C4×C17C25
hypercenterC22×#117D17
hypocenterC17C2×#2873
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×#117

3342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1032967);