Finite Group Databasebeta

C2×D6616 #40996501

order26464
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×D6616

Splittings

FittingC2×C8×C827 ⋊ C2
SylowC827 ⋊ C2×D8

Subgroups

subgroupG/H
centerC22D3308
commutator, cosocleC4×C827C23
FrattiniC4C22×D827
FittingC2×C8×C827C2
socleC22×C827D4
hypercenterC2×C8D827
hypocenterC827C2×D8
LCSG ▷ C4×C827 ▷ C2×C827 ▷ C827
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13232

Conjugacy classes & character table

6622 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26464, 157);