Finite Group Databasebeta

C2×#22568457 #31062115

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27

Aliases

direct productC2×#22568457

Splittings

SylowC67 ⋊ C2×#2839

Subgroups

subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#398×C67C2
socle, prime radicalC24×C67C24
hypercenterC2×#398D67
hypocenterC67C2×#2839
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#398

1654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

1504 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 375852);