Finite Group Databasebeta

C2×#13110088 #15693025

order3296
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13110088

Splittings

FittingC2×C8×C103 ⋊ C2
SylowC103 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D103
commutatorC2×C103C22×C4
FrattiniC4C22×D103
FittingC2×C8×C103C2
socleC22×C103C2×C4
prime radicalC22×D103C4
cosocleC4×C103C23
hypercenterC2×C8D103
hypocenterC103C2×M16
LCSG ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1648

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3296, 150);