Finite Group Databasebeta

C2×#14526868 #16949183

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

Aliases

direct productC2×#14526868

Splittings

SylowC17 ⋊ C2×#1377

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic17
commutatorC22×C17C2×C4×C8
FrattiniC22×C8C22×D17
FittingC22×C17×#97C2
socleC23×C17C22⋊C8
prime radicalC24×C17C2×C8
cosocleC22×C8×C17C23
hypercenterC22×#97D17
hypocenterC17C2×#1377
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×#97

630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 84427);