Finite Group Databasebeta

C2×#27165811 #38787169

order25664
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27165811

Splittings

SylowC401 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C4C2×#13107944
commutatorC2×C401C22×C8
FrattiniC4C22×#13107944
FittingC22×C4×C401C4
socleC22×C401C2×C8
prime radicalC23×C401C8
cosocle#15691999C23
hypercenterC22×C4#13107944
hypocenterC401C2×M32
LCSG ▷ C2×C401 ▷ C401
UCSC1 ◁ C2×C4 ◁ C22×C4

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12832

Conjugacy classes & character table

1640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25664, 1604);