Finite Group Databasebeta

C2×#22562384 #31010566

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

Aliases

direct productC2×#22562384

Splittings

FittingC2×#365×C67 ⋊ C2
SylowC67 ⋊ C2×#2231

Subgroups

subgroupG/H
centerC22#16863685
commutator, cosocleC2×C8×C67C24
FrattiniC2×C8C23×D67
FittingC2×#365×C67C2
socleC22×C67#476
prime radicalC2×#14524065C22
hypercenterC2×#365D67
hypocenterC67C2×#2231
LCSG ▷ C2×C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 324303);