Finite Group Databasebeta

← Prev (#34014688) Next (#34014690) →

C4⋊C4×C4⋊#64408 #34014689

order18688
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4⋊C4×C4⋊#64408

Splittings

FittingC4×C4⋊C4×C73 ⋊ C4
SylowC73 ⋊ C4⋊C42

Subgroups

subgroupG/H
center, FrattiniC23C23×#64408
commutatorC22×C73C22×C42
FittingC4×C4⋊C4×C73C4
socleC23×C73C23×C4
prime radical, cosocleC23×D73C24
hypercenterC4×C4⋊C4#64408
hypocenterC73C4⋊C42
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4

1838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1098273);