Finite Group Databasebeta

C2×#22562236 #31010001

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

Aliases

direct productC2×#22562236

Splittings

FittingC2×#355×C67 ⋊ C2
SylowC67 ⋊ C2×#2204

Subgroups

subgroupG/H
centerC22#16863584
commutator, cosocleC2×Q8×C67C24
FrattiniC2×Q8C23×D67
FittingC2×#355×C67C2
socleC22×C67B(4,𝔽2)
hypercenterC2×#355D67
hypocenterC67C2×#2204
LCSG ▷ C2×Q8×C67 ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 323738);