Finite Group Databasebeta

D8×C22⋊#64408 #34026180

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

Aliases

direct productD8×C22⋊#64408

Splittings

FittingC22×D8×C73 ⋊ C4
SylowC73 ⋊ C22⋊C4×D8

Subgroups

subgroupG/H
centerC22C2×D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
FittingC22×D8×C73C4
socleC22×C73C2×C4×D4
prime radicalC22×D8×D73C2
cosocleC2×C4×D73C24
hypercenterC22×D8#64408
hypocenterC73C22⋊C4×D8
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1109764);