Finite Group Databasebeta

C2×#14526864 #16949171

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14526864

Splittings

SylowC17 ⋊ C2×#1375

Subgroups

subgroupG/H
centerC22×C4C4×Dic17
commutatorC4×C17C2×C4×C8
FrattiniC22×C8C22×D17
FittingC22×C17×#97C2
socleC23×C17#97
prime radicalC24×C17M16
cosocleC22×C8×C17C23
hypercenterC22×#97D17
hypocenterC17C2×#1375
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×#97

630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84415);