Finite Group Databasebeta

C4×D4372 #46854071

order34976
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×D4372

Splittings

FittingC42×C1093 ⋊ C2
SylowC1093 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D1093
commutatorC2×C1093C22×C4
FrattiniC22C22×D1093
FittingC42×C1093C2
socle, cosocleC22×C1093C23
prime radicalC2×D4372C2
hypercenterC42D1093
hypocenterC1093C4×D4
LCSG ▷ C2×C1093 ▷ C1093
UCSC1 ◁ C2×C4 ◁ C42

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17488

Conjugacy classes & character table

8756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34976, 110);