Finite Group Databasebeta

C22×#11758194 #16840522

order3904
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11758194

Splittings

SylowC61 ⋊ C22×M16

Subgroups

subgroupG/H
centerC22×C4C2×D61
commutatorC2×C61C23×C4
FrattiniC4C23×D61
FittingC23×C4×C61C2
socleC23×C61C2×C4
prime radicalC24×C61C4
cosocleC4×C61C24
hypercenterC23×C4D61
hypocenterC61C22×M16
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

1000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 1309);