Finite Group Databasebeta

C22×(C2×D443)⋊C4 #43248164

order28352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D443)⋊C4

Splittings

FittingC23×C4×C443 ⋊ C2
SylowC443 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D443
commutatorC2×C443C23×C4
FrattiniC22C23×D443
FittingC23×C4×C443C2
socleC24×C443C22
prime radicalC24×D443C2
cosocleC22×C443C24
hypercenterC23×C4D443
hypocenterC443C22×C22⋊C4
LCSG ▷ C2×C443 ▷ C443
UCSC1 ◁ C24 ◁ C23×C4

674 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, 996);