Finite Group Databasebeta

D4×D73⋊M16 #34031353

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD4×D73⋊M16
unambiguous semidirect productD73⋊(D4×M16)

Splittings

SylowC73 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC2×C4C23×#64408
commutator, socleC22×C73C24×C4
FrattiniC22C24×#64408
FittingC2×C4×D4×C73C4
prime radicalC22×D4×D73C4
cosocleC2×Dic73C25
hypercenterC2×C4×D4#64408
hypocenterC73C2×D4×M16
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

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, 1114937);