Finite Group Databasebeta

C2×#27163157 #38763506

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

Aliases

direct productC2×#27163157

Splittings

SylowC397 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊#13097544
commutatorC22×C397C22×C4
FrattiniC22C22×#13097544
FittingC22×C4×C397C4
socleC22×C397C22⋊C4
prime radicalC23×C397C2×C4
cosocleC2×Dic397C23
hypercenterC22×C4#13097544
hypocenterC397C2×#101
LCSG ▷ C22×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

1606 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1533);