Finite Group Databasebeta

C22×#11758201 #16840534

order3904
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11758201

Splittings

FittingC22×Q8×C61 ⋊ C2
SylowC61 ⋊ C22×SD16

Subgroups

subgroupG/H
centerC23C22⋊D61
commutator, cosocleC4×C61C24
FrattiniC4C23×D61
FittingC22×Q8×C61C2
socleC23×C61D4
prime radicalC22×D244C2
hypercenterC22×Q8D61
hypocenterC61C22×SD16
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 1321);