Finite Group Databasebeta

D4×#92420 #16840788

order3904
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD4×#92420

Splittings

SylowC61 ⋊ C8×D4

Subgroups

subgroupG/H
center, FrattiniC22C22×#6923
commutatorC2×C61C22×C8
Fitting, prime radicalC2×D4×C61C4
socleC22×C61C22×C4
cosocleC2×Dic61C23
hypercenterC2×D4#6923
hypocenterC61C8×D4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×D4

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 1575);