Finite Group Databasebeta

C2×#14526765 #16944138

order4352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14526765

Splittings

SylowC17 ⋊ C2×#1338

Subgroups

subgroupG/H
centerC22×C4#63227
commutatorC2×C4×C17C22×C8
FrattiniC4×C8C22×D17
FittingC2×C17×C4⋊C16C2
socle, prime radicalC23×C17C22⋊C8
cosocleC4×C8×C17C23
hypercenterC2×C4⋊C16D17
hypocenterC17C2×#1338
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C4⋊C16

346 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, 79382);