Finite Group Databasebeta

C2×#28381796 #43247665

order28352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28381796

Splittings

SylowC443 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D443
commutatorC2×C443C2×C42
FrattiniC2×C4C22×D443
FittingC22×C8×C443C2
socle, prime radicalC23×C443C2×C4
cosocleC2×C4×C443C23
hypercenterC22×C8D443
hypocenterC443C2×#97
LCSG ▷ C2×C443 ▷ C443
UCSC1 ◁ C22×C4 ◁ C22×C8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28352

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, 497);