Finite Group Databasebeta

C2×#28413624 #44440783

order29408
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28413624

Splittings

FittingC2×C8×C919 ⋊ C2
SylowC919 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D919
commutatorC2×C919C22×C4
FrattiniC4C22×D919
FittingC2×C8×C919C2
socleC22×C919C2×C4
prime radicalC22×D919C4
cosocleC4×C919C23
hypercenterC2×C8D919
hypocenterC919C2×M16
LCSG ▷ C2×C919 ▷ C919
UCSC1 ◁ C2×C4 ◁ C2×C8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14704

Conjugacy classes & character table

7364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29408, 150);