Finite Group Databasebeta

C2×(C22⋊D167)⋊C8 #36332808

order21376
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×(C22⋊D167)⋊C8

Splittings

FittingC2×C22⋊C8×C167 ⋊ C2
SylowC167 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×D167
commutatorC2×C167C23×C8
FrattiniC2×C4C23×D167
FittingC2×C22⋊C8×C167C2
socleC23×C167C22×C4
prime radicalC22×C22⋊D167C4
cosocleC2×C4×C167C24
hypercenterC2×C22⋊C8D167
hypocenterC167C2×C8×D4
LCSG ▷ C2×C167 ▷ C167
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

616 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, 13180);