Finite Group Databasebeta

C22×Dic254 #16861249

order4064
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic254

Splittings

SylowC127 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D127
commutator, cosocleC2×C127C24
FrattiniC2C23×D127
FittingC22×C4×C127C2
socle, prime radicalC23×C127C22
hypercenterC22×C4D127
hypocenterC127C22×Q8
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C22×C4

156 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, 186);