Finite Group Databasebeta

C2×#26018379 #36469407

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

Aliases

direct productC2×#26018379

Splittings

SylowC89 ⋊ C2×#1394

Subgroups

subgroupG/H
centerC23#15667927
commutatorC2×C4×C89C2×C42
FrattiniC22×Q8C22×D89
FittingC2×#391×C89C2
socleC23×C89#99
prime radicalC24×C89C22⋊C4
cosocleC22×Q8×C89C23
hypercenterC2×#391D89
hypocenterC89C2×#1394
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C24 ◁ C23×Q8 ◁ C2×#391

818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

2516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 84547);