Finite Group Databasebeta

C2×#26019394 #36530306

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

Aliases

direct productC2×#26019394

Splittings

SylowC89 ⋊ C2×#1633

Subgroups

subgroupG/H
centerC23#15667982
commutator, cosocleC42×C89C24
FrattiniC42C23×D89
FittingC2×Q8⋊C8×C89C2
socle, prime radicalC23×C89#120
hypercenterC2×Q8⋊C8D89
hypocenterC89C2×#1633
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

1010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22784

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, 145446);