Finite Group Databasebeta

C2×#22562213 #31009864

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22562213

Splittings

FittingC2×#458×C67 ⋊ C2
SylowC67 ⋊ C2×#2200

Subgroups

subgroupG/H
centerC22#16863582
commutator, cosocleC2×D4×C67C24
FrattiniC2×D4C23×D67
FittingC2×#458×C67C2
socleC22×C67B(4,𝔽2)
hypercenterC2×#458D67
hypocenterC67C2×#2200
LCSG ▷ C2×D4×C67 ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#458

1328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 323601);