Finite Group Databasebeta

C2×#14529247 #17036143

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

Aliases

direct productC2×#14529247

Splittings

FittingC23×M16×C17 ⋊ C2
SylowC17 ⋊ C2×#1900

Subgroups

subgroupG/H
centerC23C2×#63227
commutatorC23×C17C23×C4
FrattiniC22×C4C23×D17
FittingC23×M16×C17C2
socleC23×C17C2×C22⋊C4
prime radicalC22×#10587616C2
cosocleC22×C4×C17C24
hypercenterC23×M16D17
hypocenterC17C2×#1900
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×M16

2198 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, 171387);