Finite Group Databasebeta

C4×Dic188 #15689219

order3008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic188

Splittings

SylowC47 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC2×C4D188
commutatorC4×C47C22×C4
FrattiniC2×C4C22×D47
FittingC4×C8×C47C2
socle, prime radicalC22×C47C2×D4
cosocleC2×C4×C47C23
hypercenterC4×C8D47
hypocenterC47C4×Q16
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3008

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 645);