Finite Group Databasebeta

C4⋊C8×D292 #33104007

order18688
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C8×D292

Splittings

FittingC4×C4⋊C8×C73 ⋊ C2
SylowC73 ⋊ D4×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D73
commutatorC22×C73C23×C8
FittingC4×C4⋊C8×C73C2
socleC23×C73C23×C4
prime radicalC22×D292C2×C4
cosocleC22×C4×C73C24
hypercenterC4×C4⋊C8D73
hypocenterC73D4×C4⋊C8
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C8

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

2980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 187591);