Finite Group Databasebeta

C4×#19153342 #37526913

order22976
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#19153342

Splittings

FittingC4×Q8×C359 ⋊ C2
SylowC359 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D359
commutatorC2×C359C23×C4
FrattiniC22C23×D359
FittingC4×Q8×C359C2
socle, cosocleC22×C359C24
prime radicalC2×#19153342C2
hypercenterC4×Q8D359
hypocenterC359C4×#41
LCSG ▷ C2×C359 ▷ C359
UCSC1 ◁ C2×C4 ◁ C4×Q8

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11488

Conjugacy classes & character table

3620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 1019);