Finite Group Databasebeta

C2×#24923139 #36326539

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

Aliases

direct productC2×#24923139

Splittings

SylowC167 ⋊ C2×#384

Subgroups

subgroupG/H
centerC24C22×D167
commutatorC22×C167C23×C4
FrattiniC23C23×D167
FittingC22×C42×C167C2
socle, prime radicalC24×C167C23
cosocleC23×C167C24
hypercenterC22×C42D167
hypocenterC167C2×#384
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C24 ◁ C22×C42

888 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21376

Conjugacy classes & character table

5368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 6911);