Finite Group Databasebeta

C2×#14555497 #17984101

order4384
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14555497

Splittings

FittingC2×Q8×C137 ⋊ C2
SylowC137 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D137
commutator, cosocleC4×C137C23
FrattiniC4C22×D137
FittingC2×Q8×C137C2
socleC22×C137D4
prime radicalC2×D548C2
hypercenterC2×Q8D137
hypocenterC137C2×SD16
LCSG ▷ C4×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4384, 159);