Finite Group Databasebeta

C2×#14526756 #16944106

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

Aliases

direct productC2×#14526756

Splittings

FittingC2×C17×#364 ⋊ C2
SylowC17 ⋊ C2×#1335

Subgroups

subgroupG/H
centerC2×C8#63228
commutatorC8×C17C22×C8
FrattiniC4×C8C22×D17
FittingC2×C17×#364C2
socleC22×C17D4⋊C8
prime radicalC2×#10587590C4
cosocleC4×C8×C17C23
hypercenterC2×#364D17
hypocenterC17C2×#1335
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×#364

414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 79350);