Finite Group Databasebeta

C2×#14529695 #17038319

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14529695

Splittings

SylowC17 ⋊ C2×#1978

Subgroups

subgroupG/H
centerC23#10587624
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC23×D8×C17C2
socleC23×C17#121
cosocleC22×C4×C17C24
hypercenterC23×D8D17
hypocenterC17C2×#1978
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D8

1694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 173563);