Finite Group Databasebeta

← Prev (#34033289) Next (#34033291) →

C4×#17989677 #34033290

order18688
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#17989677
unambiguous semidirect product#64408⋊#335

Splittings

FittingC4×C8×C73 ⋊ C8
SylowC73 ⋊ C4×#335

Subgroups

subgroupG/H
centerC2×C4C4⋊#10596842
commutatorC4×C73C2×C4×C8
FrattiniC2×C4C22×#10596842
FittingC4×C8×C73C8
socleC22×C73C2×C4⋊C8
prime radicalC22×D73C2×C4⋊C4
cosocleC2×C4×#64408C23
hypercenterC4×C8#10596842
hypocenterC73C4×#335
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1116874);