Finite Group Databasebeta

C2×#22568753 #31719427

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#22568753

Splittings

FittingC22×#104×C67 ⋊ C2
SylowC67 ⋊ C2×#2901

Subgroups

subgroupG/H
centerC2×C4C2×D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC22×#104×C67C2
socleC22×C67C22×C22⋊C4
prime radicalC2×#16864232C2
cosocleC2×C4×C67C25
hypercenterC22×#104D67
hypocenterC67C2×#2901
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

4946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1936 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033164);