Finite Group Databasebeta

C2×#24923166 #36326588

order21376
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#24923166

Splittings

SylowC167 ⋊ C2×#389

Subgroups

subgroupG/H
centerC24C22×D167
commutatorC22×C167C23×C4
FrattiniC23C23×D167
FittingC2×#95×C167C2
socle, prime radicalC24×C167C23
cosocleC23×C167C24
hypercenterC2×#95D167
hypocenterC167C2×#389
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C24 ◁ C2×#95

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21376

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, 6960);