Finite Group Databasebeta

C2×#24923686 #36337237

order21376
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#24923686

Splittings

SylowC167 ⋊ C2×#504

Subgroups

subgroupG/H
centerC2×C8C22×D167
commutatorC2×C167C23×C8
FrattiniC8C23×D167
FittingC2×#131×C167C2
socleC22×C167C22×C8
prime radicalC2×#41×C167C4
cosocleC8×C167C24
hypercenterC2×#131D167
hypocenterC167C2×#504
LCSG ▷ C2×C167 ▷ C167
UCSC1 ◁ C2×C8 ◁ C2×#131

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10688

Conjugacy classes & character table

3400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 17609);