Finite Group Databasebeta

C2×#26018149 #36444653

order22784
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#26018149

Splittings

SylowC89 ⋊ C2×#1301

Subgroups

subgroupG/H
centerC22×C4#13083551
commutatorC2×C4×C89C2×C42
FrattiniC2×C42C22×D89
FittingC22×C4⋊C8×C89C2
socleC23×C89#95
prime radicalC24×C89C4⋊C4
cosocleC2×C42×C89C23
hypercenterC22×C4⋊C8D89
hypocenterC89C2×#1301
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4⋊C8

666 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11392

Conjugacy classes & character table

3596 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 59793);