Finite Group Databasebeta

C2×#27160917 #38745013

order25216
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27160917

Splittings

SylowC197 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22#20263267
commutator, cosocleC16×C197C23
FrattiniC16C22×D197
Fitting, prime radicalC2×D16×C197C2
socleC22×C197D16
hypercenterC2×D16D197
hypocenterC197C2×SD64
LCSG ▷ C16×C197 ▷ C8×C197 ▷ C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D16

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12608

Conjugacy classes & character table

2194 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 6811);