Finite Group Databasebeta

C2×D7736 #44526132

order30944
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×D7736

Splittings

FittingC2×C8×C967 ⋊ C2
SylowC967 ⋊ C2×D8

Subgroups

subgroupG/H
centerC22D3868
commutator, cosocleC4×C967C23
FrattiniC4C22×D967
FittingC2×C8×C967C2
socleC22×C967D4
hypercenterC2×C8D967
hypocenterC967C2×D8
LCSG ▷ C4×C967 ▷ C2×C967 ▷ C967
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15472

Conjugacy classes & character table

7742 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30944, 157);