Finite Group Databasebeta

C2×#26022604 #36712632

order22784
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#26022604

Splittings

FittingC2×C4×C22⋊C4×C89 ⋊ C2
SylowC89 ⋊ C2×#2273

Subgroups

subgroupG/H
centerC24C23×D89
commutatorC2×C89C23×C42
FrattiniC23C24×D89
FittingC2×C4×C22⋊C4×C89C2
socleC24×C89C24
prime radicalC25×D89C22
cosocleC23×C89C25
hypercenterC2×C4×C22⋊C4D89
hypocenterC89C2×#2273
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

5790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5696

Conjugacy classes & character table

3656 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 327772);