Finite Group Databasebeta

C2×#14543642 #17950857

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#14543642

Splittings

SylowC17 ⋊ C2×#1287

Subgroups

subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC2×C17×C22⋊C8C4
socleC23×C17#95
prime radicalC24×C17C4⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×C22⋊C8#595
hypocenterC17C2×#1287
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1086101);