Finite Group Databasebeta

C2×#29509155 #44526126

order30944
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#29509155

Splittings

SylowC967 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D967
commutatorC2×C967C22×C4
FrattiniC4C22×D967
FittingC22×C4×C967C2
socleC22×C967C2×C4
prime radicalC23×C967C4
cosocleC4×C967C23
hypercenterC22×C4D967
hypocenterC967C2×M16
LCSG ▷ C2×C967 ▷ C967
UCSC1 ◁ C2×C4 ◁ C22×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15472

Conjugacy classes & character table

7748 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30944, 151);