Finite Group Databasebeta

C2×#28381822 #43247763

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

Aliases

direct productC2×#28381822

Splittings

SylowC443 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D1772
commutatorC4×C443C22×C4
FrattiniC2×C4C22×D443
FittingC22×C8×C443C2
socleC22×C443C4⋊C4
prime radicalC23×C443Q8
cosocleC2×C4×C443C23
hypercenterC22×C8D443
hypocenterC443C2×#108
LCSG ▷ C4×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14176

Conjugacy classes & character table

7100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28352, 595);