Finite Group Databasebeta

C2×#14529578 #17037903

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#14529578

Splittings

FittingC22×C4×C8×C17 ⋊ C2
SylowC17 ⋊ C2×#1954

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC22×C17C23×C8
FrattiniC22×C4C23×D17
FittingC22×C4×C8×C17C2
socleC24×C17C22×C4
prime radicalC23×D68C4
cosocleC22×C4×C17C24
hypercenterC22×C4×C8D17
hypocenterC17C2×#1954
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×C4×C8

2158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 173147);