Finite Group Databasebeta

C2×#28381807 #43247704

order28352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#28381807

Splittings

SylowC443 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23C22⋊D443
commutatorC4×C443C22×C4
FrattiniC2×C4C22×D443
Fitting, prime radicalC22×D4×C443C2
socleC23×C443D4
cosocleC2×C4×C443C23
hypercenterC22×D4D443
hypocenterC443C2×#102
LCSG ▷ C4×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14176

Conjugacy classes & character table

4448 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28352, 536);