Finite Group Databasebeta

C2×#26018344 #36469305

order22784
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#26018344

Splittings

SylowC89 ⋊ C2×#1380

Subgroups

subgroupG/H
centerC24D712
commutatorC8×C89C2×C42
FrattiniC22×C8C22×D89
FittingC23×C16×C89C2
socle, prime radicalC24×C89D8
cosocleC22×C8×C89C23
hypercenterC23×C16D89
hypocenterC89C2×#1380
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8 ◁ C23×C16

694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22784

Conjugacy classes & character table

5720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 84445);