Finite Group Databasebeta

C2×#26021606 #36582559

order22784
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#26021606

Splittings

SylowC89 ⋊ C2×#2062

Subgroups

subgroupG/H
centerC23#15667982
commutator, cosocleC24×C89C24
FrattiniC24C23×D89
FittingC2×#342×C89C2
socleC23×C89#120
prime radicalC25×C89C23
hypercenterC2×#342D89
hypocenterC89C2×#2062
LCSG ▷ C24×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

1614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 197699);