Finite Group Databasebeta

C2×#24923157 #36326567

order21376
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#24923157

Splittings

SylowC167 ⋊ C2×#388

Subgroups

subgroupG/H
centerC24C22×D167
commutatorC22×C167C23×C4
FrattiniC23C23×D167
FittingC22×C22⋊C4×C167C2
socleC24×C167C23
prime radicalC25×C167C22
cosocleC23×C167C24
hypercenterC22×C22⋊C4D167
hypocenterC167C2×#388
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C24 ◁ C22×C22⋊C4

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10688

Conjugacy classes & character table

3376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 6939);