Finite Group Databasebeta

C2×#14526666 #16924372

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14526666

Splittings

SylowC17 ⋊ C2×#1295

Subgroups

subgroupG/H
centerC24#63227
commutatorC2×C4×C17C2×C42
FrattiniC2×C42C22×D17
FittingC22×C17×#97C2
socle, prime radicalC24×C17C22⋊C4
cosocleC2×C42×C17C23
hypercenterC22×#97D17
hypocenterC17C2×#1295
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#97

830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 59616);