Finite Group Databasebeta

C2×#27163165 #38763531

order25408
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27163165
unambiguous semidirect productD397⋊#107

Splittings

FittingC2×C8×C397 ⋊ C4
SylowC397 ⋊ C2×#107

Subgroups

subgroupG/H
centerC22C4⋊#13097544
commutatorC4×C397C22×C4
FrattiniC4C22×#13097544
FittingC2×C8×C397C4
socleC22×C397C4⋊C4
prime radicalC22×D397D4
cosocleC4×D397C23
hypercenterC2×C8#13097544
hypocenterC397C2×#107
LCSG ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6352

Conjugacy classes & character table

1612 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1558);