Finite Group Databasebeta

C2×#24923033 #36323861

order21376
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#24923033

Splittings

SylowC167 ⋊ C2×#341

Subgroups

subgroupG/H
centerC22×C4C22⋊D167
commutatorC4×C167C2×C42
FrattiniC22×C4C22×D167
FittingC22×M16×C167C2
socleC23×C167C4⋊C4
prime radicalC24×C167Q8
cosocleC22×C4×C167C23
hypercenterC22×M16D167
hypocenterC167C2×#341
LCSG ▷ C4×C167 ▷ C2×C167 ▷ C167
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

392 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, 4233);