Finite Group Databasebeta

C2×#22562425 #31010717

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

Aliases

direct productC2×#22562425

Splittings

FittingC2×#365×C67 ⋊ C2
SylowC67 ⋊ C2×#2238

Subgroups

subgroupG/H
centerC22#16863716
commutator, cosocleC2×C8×C67C24
FrattiniC2×C8C23×D67
FittingC2×#365×C67C2
socleC22×C67#481
prime radicalC2×#16863650C2
hypercenterC2×#365D67
hypocenterC67C2×#2238
LCSG ▷ C2×C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1096 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 324454);