Finite Group Databasebeta

C2×#27160821 #38741296

order25216
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27160821

Splittings

SylowC197 ⋊ C2×#330

Subgroups

subgroupG/H
centerC23C22⋊Dic197
commutatorC2×C4×C197C22×C4
FrattiniC42C22×D197
FittingC2×#125×C197C2
socle, prime radicalC23×C197C22⋊C4
cosocleC42×C197C23
hypercenterC2×#125D197
hypocenterC197C2×#330
LCSG ▷ C2×C4×C197 ▷ C22×C197 ▷ C197
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25216

Conjugacy classes & character table

2782 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 3094);