Finite Group Databasebeta

C4×#17989460 #34008275

order18688
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#17989460

Splittings

FittingC4×C4⋊C4×C73 ⋊ C4
SylowC73 ⋊ C4×#340

Subgroups

subgroupG/H
centerC22×C4C22⋊#64408
commutatorC4×C73C43
FrattiniC22×C4C22×#64408
FittingC4×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C2×D4
cosocleC22×C4×D73C23
hypercenterC4×C4⋊C4#64408
hypocenterC73C4×#340
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1091859);