Finite Group Databasebeta

C2×#27163041 #38762947

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

Aliases

direct productC2×#27163041

Splittings

FittingC2×C16×C397 ⋊ C2
SylowC397 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22D3176
commutator, cosocleC8×C397C23
FrattiniC8C22×D397
FittingC2×C16×C397C2
socleC22×C397D8
prime radicalC2×D3176C2
hypercenterC2×C16D397
hypocenterC397C2×SD32
LCSG ▷ C8×C397 ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

6358 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 974);