Finite Group Databasebeta

C2×#27160460 #38737972

order25184
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27160460

Splittings

SylowC787 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D787
commutatorC2×C787C22×C4
FrattiniC4C22×D787
FittingC22×C4×C787C2
socleC22×C787C2×C4
prime radicalC23×C787C4
cosocleC4×C787C23
hypercenterC22×C4D787
hypocenterC787C2×M16
LCSG ▷ C2×C787 ▷ C787
UCSC1 ◁ C2×C4 ◁ C22×C4

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12592

Conjugacy classes & character table

6308 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25184, 151);