Finite Group Databasebeta

C22×#19150714 #36378234

order22592
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#19150714

Splittings

FittingC23×C4×C353 ⋊ C2
SylowC353 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D353
commutatorC2×C353C23×C4
FrattiniC22C23×D353
FittingC23×C4×C353C2
socleC24×C353C22
prime radicalC24×D353C2
cosocleC22×C353C24
hypercenterC23×C4D353
hypocenterC353C22×C22⋊C4
LCSG ▷ C2×C353 ▷ C353
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11296

Conjugacy classes & character table

5672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22592, 996);