Finite Group Databasebeta

C2×#14526735 #16943509

order4352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14526735

Splittings

SylowC17 ⋊ C2×#1327

Subgroups

subgroupG/H
centerC2×C4#10587505
commutatorC2×C4×C17C22×C8
FrattiniC2×M16C22×D17
FittingC2×C17×#423C2
socleC22×C17#324
prime radicalC24×C17M16
cosocleC2×M16×C17C23
hypercenterC2×#423D17
hypocenterC17C2×#1327
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#423

410 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 78753);