Finite Group Databasebeta

C2×#24924105 #36338946

order21376
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC2×#24924105

Splittings

FittingC22×#41×C167 ⋊ C2
SylowC167 ⋊ C2×#585

Subgroups

subgroupG/H
centerC2×C4C23×D167
commutator, cosocleC2×C167C26
FrattiniC2C25×D167
FittingC22×#41×C167C2
socleC22×C167C25
hypercenterC22×#41D167
hypocenterC167C2×#585
LCSG ▷ C2×C167 ▷ C167
UCSC1 ◁ C2×C4 ◁ C22×#41

5956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5344

Conjugacy classes & character table

3388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 19318);