Finite Group Databasebeta

C2×C67⋊#1304 #30746150

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C26

Aliases

direct productC2×C67⋊#1304
unambiguous semidirect product(C2×C67)⋊#1304

Splittings

SylowC67 ⋊ C2×#1304

Subgroups

subgroupG/H
centerC23C67⋊#95
commutatorC23×C67C2×C42
FrattiniC25C22×D67
FittingC2×#379×C67C2
socleC23×C67#95
prime radicalC26×C67C22
cosocleC25×C67C23
hypercenterC2×#379D67
hypocenterC67C2×#1304
LCSG ▷ C23×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C26 ◁ C2×#379

2414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 59887);