Finite Group Databasebeta

C2×#13110090 #15693031

order3296
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13110090

Splittings

FittingC2×D4×C103 ⋊ C2
SylowC103 ⋊ C2×D8

Subgroups

subgroupG/H
centerC22C22⋊D103
commutator, cosocleC4×C103C23
FrattiniC4C22×D103
FittingC2×D4×C103C2
socleC22×C103D4
hypercenterC2×D4D103
hypocenterC103C2×D8
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1648

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3296, 156);