Finite Group Databasebeta

C2×#26019300 #36526678

order22784
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#26019300

Splittings

SylowC89 ⋊ C2×#1618

Subgroups

subgroupG/H
centerC23#15667981
commutator, cosocleC22×C4×C89C24
FrattiniC22×C4C23×D89
Fitting, prime radicalC2×#538×C89C2
socleC23×C89#120
hypercenterC2×#538D89
hypocenterC89C2×#1618
LCSG ▷ C22×C4×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#538

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

1982 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 141818);