Finite Group Databasebeta

C2×#28381805 #43247697

order28352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28381805

Splittings

SylowC443 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic443
commutatorC22×C443C22×C4
FrattiniC2×C4C22×D443
FittingC22×Q8×C443C2
socleC22×C443C22⋊C4
prime radicalC23×C443C2×C4
cosocleC2×C4×C443C23
hypercenterC22×Q8D443
hypocenterC443C2×#101
LCSG ▷ C22×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14176

Conjugacy classes & character table

4442 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28352, 529);