Finite Group Databasebeta

C2×#14529495 #17037066

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14529495

Splittings

FittingC22×C17×#97 ⋊ C2
SylowC17 ⋊ C2×#1938

Subgroups

subgroupG/H
centerC22×C4C2×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×#97C2
socleC23×C17C4×D4
prime radicalC22×#63252C22
cosocleC22×C4×C17C24
hypercenterC22×#97D17
hypocenterC17C2×#1938
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×#97

1074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 172310);