Finite Group Databasebeta

C2×#27165729 #38786636

order25664
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#27165729

Splittings

SylowC401 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D401
commutator, cosocleC22×C401C24
FrattiniC22C23×D401
FittingC2×C42×C401C2
socle, prime radicalC23×C401C23
hypercenterC2×C42D401
hypocenterC401C2×#125
LCSG ▷ C22×C401 ▷ C401
UCSC1 ◁ C23 ◁ C2×C42

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25664

Conjugacy classes & character table

6428 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25664, 1071);