Finite Group Databasebeta

C4×Dic254 #16861175

order4064
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic254

Splittings

SylowC127 ⋊ C4×Q8

Subgroups

subgroupG/H
centerC2×C4C2×D127
commutatorC2×C127C22×C4
FrattiniC22C22×D127
FittingC42×C127C2
socle, prime radical, cosocleC22×C127C23
hypercenterC42D127
hypocenterC127C4×Q8
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C42

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4064

Conjugacy classes & character table

1028 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4064, 112);