Finite Group Databasebeta

C2×#26021390 #36581707

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

Aliases

direct productC2×#26021390

Splittings

SylowC89 ⋊ C2×#2024

Subgroups

subgroupG/H
centerC24C2×C22⋊D89
commutator, cosocleC22×C4×C89C24
FrattiniC22×C4C23×D89
FittingC22×C4⋊Q8×C89C2
socle, prime radicalC24×C89C2×D4
hypercenterC22×C4⋊Q8D89
hypocenterC89C2×#2024
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊Q8

1518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22784

Conjugacy classes & character table

2528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 196847);