Finite Group Databasebeta

C2×#28381826 #43248132

order28352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28381826

Splittings

SylowC443 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D443
commutatorC2×C443C22×C8
FrattiniC8C22×D443
FittingC22×C8×C443C2
socleC22×C443C2×C8
prime radicalC23×C443C8
cosocleC8×C443C23
hypercenterC22×C8D443
hypocenterC443C2×M32
LCSG ▷ C2×C443 ▷ C443
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14176

Conjugacy classes & character table

7112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28352, 964);