Finite Group Databasebeta

C2×#14529098 #17035521

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

Aliases

direct productC2×#14529098

Splittings

FittingC22×C17×#102 ⋊ C2
SylowC17 ⋊ C2×#1874

Subgroups

subgroupG/H
centerC24D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×#102C2
socleC24×C17C2×D4
prime radicalC22×#10587624C2
cosocleC22×C4×C17C24
hypercenterC22×#102D17
hypocenterC17C2×#1874
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

2614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 170765);