Finite Group Databasebeta

C2×#14526968 #16954775

order4352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14526968

Splittings

SylowC17 ⋊ C2×#1417

Subgroups

subgroupG/H
centerC2×C4#10587497
commutatorC16×C17C22×C4
FrattiniC2×C16C22×D17
Fitting, prime radicalC2×C17×#508C2
socleC22×C17#357
cosocleC2×C16×C17C23
hypercenterC2×#508D17
hypocenterC17C2×#1417
LCSG ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×#508

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 90019);