Finite Group Databasebeta

C2×C8×D116 #16828166

order3712
isoclinismisoclinic class of Dic58
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C8×D116

Splittings

FittingC2×C4×C8×C29 ⋊ C2
SylowC29 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C8C2×D29
commutatorC2×C29C23×C8
FrattiniC2×C4C23×D29
FittingC2×C4×C8×C29C2
socleC23×C29C22×C4
prime radicalC22×D116C4
cosocleC2×C4×C29C24
hypercenterC2×C4×C8D29
hypocenterC29C2×C8×D4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 13184);