Finite Group Databasebeta

C2×#28385395 #43272965

order28736
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28385395

Splittings

SylowC449 ⋊ C2×#97

Subgroups

subgroupG/H
centerC23C2×#14267798
commutatorC2×C449C2×C42
FrattiniC22C22×#14267798
FittingC22×C4×C449C4
socle, prime radicalC23×C449C2×C4
cosocleC2×Dic449C23
hypercenterC22×C4#14267798
hypocenterC449C2×#97
LCSG ▷ C2×C449 ▷ C449
UCSC1 ◁ C23 ◁ C22×C4

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28736

Conjugacy classes & character table

1832 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28736, 1507);