Finite Group Databasebeta

C2×#14527138 #17000276

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

Aliases

direct productC2×#14527138

Splittings

SylowC17 ⋊ C2×#1470

Subgroups

subgroupG/H
centerC23C22⋊C4×D17
commutatorC23×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#324C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22×C4
cosocleC22×C4×C17C24
hypercenterC2×#324D17
hypocenterC17C2×#1470
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

1002 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135520);