Finite Group Databasebeta

C2×#27188253 #39905885

order25888
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27188253

Splittings

SylowC809 ⋊ C2×M16

Subgroups

subgroupG/H
centerC22C2×#15692395
commutatorC2×C809C22×C4
FrattiniC2C22×#15692395
FittingC2×C4×C809C4
socleC22×C809C2×C4
prime radicalC22×D809C4
cosocleDic809C23
hypercenterC2×C4#15692395
hypocenterC809C2×M16
LCSG ▷ C2×C809 ▷ C809
UCSC1 ◁ C22 ◁ C2×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12944

Conjugacy classes & character table

1636 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25888, 232);