Finite Group Databasebeta

C2×#14527678 #17004063

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

Aliases

direct productC2×#14527678

Splittings

SylowC17 ⋊ C2×#1591

Subgroups

subgroupG/H
centerC22×C4D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC2×C17×Q8⋊C8C2
socle, prime radicalC23×C17C4×D4
cosocleC42×C17C24
hypercenterC2×Q8⋊C8D17
hypocenterC17C2×#1591
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 139307);