Finite Group Databasebeta

C2×#27163119 #38763305

order25408
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27163119

Splittings

FittingC2×Q16×C397 ⋊ C2
SylowC397 ⋊ C2×#135

Subgroups

subgroupG/H
centerC22D4×D397
commutator, cosocleC4×C397C24
FrattiniC4C23×D397
FittingC2×Q16×C397C2
socleC22×C397C2×D4
hypercenterC2×Q16D397
hypocenterC397C2×#135
LCSG ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1332);