Finite Group Databasebeta

C2×#14555494 #17984093

order4384
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14555494

Splittings

SylowC137 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D137
commutatorC2×C137C22×C4
FrattiniC4C22×D137
FittingC22×C4×C137C2
socleC22×C137C2×C4
prime radicalC23×C137C4
cosocleC4×C137C23
hypercenterC22×C4D137
hypocenterC137C2×M16
LCSG ▷ C2×C137 ▷ C137
UCSC1 ◁ C2×C4 ◁ C22×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2192

Conjugacy classes & character table

1108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4384, 151);