Finite Group Databasebeta

C2×#14538248 #17901154

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14538248

Splittings

FittingC22×C4×D4×C17 ⋊ C2
SylowC17 ⋊ C2×#3036

Subgroups

subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C4×D4×C17C2
socleC23×C17C22×D4
hypercenterC22×C4×D4D17
hypocenterC17C2×#3036
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×D4

3242 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, 1036398);