Finite Group Databasebeta

C22×#11758417 #16858823

order3968
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11758417

Splittings

SylowC31 ⋊ C22×Q32

Subgroups

subgroupG/H
centerC23#92479
commutator, cosocleC8×C31C24
FrattiniC8C23×D31
FittingC22×Q16×C31C2
socle, prime radicalC23×C31D8
hypercenterC22×Q16D31
hypocenterC31C22×Q32
LCSG ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q16

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3968

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 17622);