Finite Group Databasebeta

C2×D4×#11924005 #33245153

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×D4×#11924005

Splittings

FittingC22×C4×D4×C73 ⋊ C2
SylowC73 ⋊ C2×D4×C22⋊C4

Subgroups

subgroupG/H
centerC24C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC22×C4×D4×C73C2
socleC24×C73C24
prime radicalC23×D4×D73C2
cosocleC23×C73C25
hypercenterC22×C4×D4D73
hypocenterC73C2×D4×C22⋊C4
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C22×C4×D4

8774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

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, 328737);