Finite Group Databasebeta

C2×#117×Dic17 #17192511

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×#117×Dic17

Splittings

SylowC17 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC2×C17C23×C42
FrattiniC23C24×D17
FittingC22×C17×#117C2
socleC24×C17C24
prime radicalC25×C17C23
cosocleC23×C17C25
hypercenterC22×#117D17
hypocenterC17C2×C4×#117
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×#117

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327755);