Finite Group Databasebeta

D4×#14556511 #33101384

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×#14556511

Splittings

FittingD4×C4⋊C4×C73 ⋊ C2
SylowC73 ⋊ D4×#102

Subgroups

subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingD4×C4⋊C4×C73C2
socleC23×C73C22×D4
prime radicalC2×D4×D292C2
cosocleC22×C4×C73C24
hypercenterD4×C4⋊C4D73
hypocenterC73D4×#102
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

2014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 184968);