Finite Group Databasebeta

C2×#28413628 #44440792

order29408
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28413628

Splittings

FittingC2×Q8×C919 ⋊ C2
SylowC919 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D919
commutator, cosocleC4×C919C23
FrattiniC4C22×D919
FittingC2×Q8×C919C2
socleC22×C919D4
prime radicalC2×D3676C2
hypercenterC2×Q8D919
hypocenterC919C2×SD16
LCSG ▷ C4×C919 ▷ C2×C919 ▷ C919
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14704

Conjugacy classes & character table

4604 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29408, 159);