Finite Group Databasebeta

C2×#14523238 #16861226

order4064
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14523238

Splittings

SylowC127 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22C22⋊D127
commutator, cosocleC4×C127C23
FrattiniC4C22×D127
FittingC2×Q8×C127C2
socle, prime radicalC22×C127D4
hypercenterC2×Q8D127
hypocenterC127C2×Q16
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4064

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4064, 163);