Finite Group Databasebeta

C2×#14529285 #17036231

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14529285

Splittings

FittingC2×C4×#41×C17 ⋊ C2
SylowC17 ⋊ C2×#1906

Subgroups

subgroupG/H
centerC2×C4#10587616
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C4×#41×C17C2
socleC22×C17#386
prime radicalC2×#11763607C2
cosocleC22×C4×C17C24
hypercenterC2×C4×#41D17
hypocenterC17C2×#1906
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×#41

1798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 171475);